Zanariah Abdul Majid

Zanariah Abdul Majid
  • Doctor of Philosophy
  • Lecturer at Universiti Putra Malaysia

About

207
Publications
76,180
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
1,657
Citations
Introduction
Prof. Dr Zanariah Abdul Majid is currently a lecturer in the Department of Mathematics, Faculty of Science at the Universiti Putra Malaysia (UPM). She has published widely in the area of numerical analysis. Her area of research is emphasis on solving ordinary differential equation, delay differential equation, boundary value problem, volterra and fredholm-integro differential equation, differential algebraic equation and higher order ODEs that will involve the multistep method.
Current institution
Universiti Putra Malaysia
Current position
  • Lecturer
Additional affiliations
March 2007 - February 2022
Universiti Putra Malaysia
Position
  • Lecturer
Editor roles

Publications

Publications (207)
Article
Full-text available
This paper describes the development of a 4-point diagonally implicit block method for solving first order Ordinary Differential Equations (ODEs) using variable step size. This method will estimate the solutions of Initial Value Problems (IVPs) at four points simultaneously. The method developed is suitable for the numerical integration of non stif...
Article
Full-text available
A new four-point implicit block multistep method is developed for solving systems of first-order ordinary differential equations with variable step size. The method computes the numerical solution at four equally spaced points simultaneously. The stability of the proposed method is investigated. The Gauss-Seidel approach is used for the implementat...
Article
Full-text available
A fourth order two-point block method is developed for solving nonlinear third order boundary value problems (BVPs) directly. The two-point block method will solve the nonlinear third order BVPs at two points simultaneously within the block. The shooting technique will use the Newton's method for checking of the convergent and the guessing values f...
Article
Full-text available
This paper considers the implementation of fourth order direct method in the form of Adams Moulton method for solving directly second order delay differential equations. The proposed method approximates the solutions using constant step size. Numerical results are presented to show that the proposed code is suitable for solving second order delay d...
Article
Full-text available
The capabilities and performances of a quadrupole ion trap under damping force based on collisional cooling is of particular importance in high-resolution mass spectrometry and should be analyzed by Mathieu's differential solutions. These solutions describe the stability and instability of the ion's trajectories confined in quadrupole devices. One...
Article
Recently, one artificial intelligence technique, known as artificial neural network (ANN), has brought advanced development to the arena of mathematical research. It competes effectively with other traditional methods in providing accurate solutions for fractional differential equations (FDEs). This work aims to implement a feedforward ANN with two...
Article
In this study, for the numerical solution of general second-order ordinary differential equations (ODEs) that exhibit oscillatory or periodic behavior, fifth- and sixth-order explicit multi-step Runge-Kutta-Nystrom (MSGRKN) methods, respectively, are constructed. The parameters of the proposed methods rely on the frequency ω of each problem whose s...
Article
In this research, the constant type of neutral delay Volterra integro-differential equations (NDVIDEs) are currently being resolved by applying the proposed technique in numerical analysis namely, two-point two off-step point block multistep method (2OBM4). This new technique is being applied in solving NDVIDE, identified as a hybrid block multiste...
Article
Full-text available
Volterra integro-differential equation with delay (VIDED) is solved using a diagonally multistep block method (DMB). This study provides the derivation of the DMB utilizing Taylor series with a constant step size strategy for treating the first order VIDED. In predictor-corrector mode, the DMB method combines the predictor and corrector formulae. I...
Article
The aim of this manuscript is to solve the initial-value problems of neutral delay Volterra integro-differential equations with constant or proportional delays. Hence, a proposed hybrid technique named as an implicit multistep block method with an off-step point (1OBM4) is formulated for the numerical solution of NDVIDE. A LMM associated with an of...
Article
The boundary and initial conditions that are related to the retarded and neutral delay differential equations, respectively, will be resolved in this work by using the previous direct multistep method. This method solves retarded and neutral delay differential equations directly by implementing the proposed method without converting it to a first-o...
Article
The neutral Volterra integro-differential equation with proportional and mixed delays (NDVIDE) is being solved by a newly proposed technique in numerical method, namely, the two-point one off-point block multistep method (1OBM3). The method is also known as a hybrid multistep block method. Subsequently, Lagrange interpolating polynomial is utilized...
Article
An intra-step block Falkner method whose coefficients depend on a parameter ω and the step length h is presented in this study for solving numerically second-order delay differential equations with oscillatory solutions. In the development of the method, the collocation and interpolation techniques were employed. The investigation of the properties...
Article
Full-text available
The delay integro-differential equation for the Volterra type has been solved by using the two-point multistep block (2PBM) method with constant step-size. The proposed block method of order three is formulated using Taylor expansion and will simultaneously approximate the numerical solution at two points. The 2PBM method is developed by combining...
Article
Fractional relaxation-oscillation equation (FROE) has proved to provide more accurate interpretation of describing materials with viscoelastic properties. However, the current operator considered is not general ones, thus restricted on giving outcome for single fractional operator only. Hilfer derivative is one of the generalized fractional operato...
Article
In this study, a variable step size formulation of multi-step general Runge–Kutta-Nyström (MSGN) methods to directly integrate general second-order initial value problems (IVPs) is considered. This formula is carried out using an embedded explicit pair where: the higher-order formula is an accurate and the lower-order formula uses to estimate the l...
Article
Artificial neural network (ANN) have shown great success in various scientific fields over several decades. Recently, one of its variants known as deep feedforward neural network (FNN) led to dramatic improvement in many tasks, including getting more accurate approximation solution for integer-order differential equations. However, its capability o...
Article
Full-text available
This article presents a numerical approach for solving the second kind of Volterra integro- differential equation (VIDE). The multistep block-Boole's rule method will estimate the solutions for the linear and nonlinear problems of VIDE. The method computes two solutions for VIDE along the interval. The proposed method is developed by derivation of...
Article
Full-text available
Fractional differential equations have recently demonstrated their importance in a variety of fields, including medicine, applied sciences, and engineering. The main objective of this study is to propose an Adams-type multistep method for solving differential equations of fractional order. The method is developed by implementing the Lagrange interp...
Article
In this study, a class of direct numerical integrators for solving special second-order ordinary differential equations (ODEs) is proposed and studied. The method is multistage and multistep in nature. This class of integrators is called "two-step Runge-Kutta-Nyström", denoted by TSRKN. The direct approach to higher-order ODEs is desirable to avoid...
Poster
Full-text available
The ICREM9 will have five Satellite Conferences: Satellite Conference on Computational Fluid Dynamics (CFD2021) Satellite Conference on Artificial Intelligence & Data-Driven Innovations (AIDDI2021) Satellite Conference on Scientific Computing, Simulation, and Quantitative Instrumentation (SCSQI2021) Satellite Conference on Structural and Analytica...
Article
Full-text available
This numerical study exclusively focused on developing a diagonally multistep block method of order five (2DDM5) to get the approximate solution of the third-order Robin boundary value problems directly. The mathematical derivation of the developed 2DDM5 method is by approximating the integrand function with Lagrange interpolation polynomial. The p...
Article
Full-text available
The aim of this research is to produce accurate numerical results in solving neutral Volterra delay integro-differential equations (NVDIDE) and retarded Volterra delay integro-differential equations (RVDIDE) of constant type. A third-order explicit multistep block method is derived by applying the Taylor series. The consistency, zero stability, and...
Article
Full-text available
This paper proposed a new alternative approach of the implicit diagonal block backward differentiation formula (BBDF) to solve linear and nonlinear first-order stiff ordinary differential equations (ODEs). We generate the solver by manipulating the numbers of back values to achieve a higher-order possible using the interpolation procedure. The algo...
Article
Full-text available
There are still mathematical predictions in the fight against epidemics. Speedy expansion, ways and procedures for pandemic control require early understanding when solutions with better computer-based mathematical modeling and prognosis are developed. Despite high uncertainty in each of these models, one of the important tools for the public healt...
Article
Full-text available
This numerical study exclusively focused on the direct two point diagonally multistep block method of order four (2DDM4) in the form of Adams-type formulas. The proposed predictor–corrector scheme was applied in this study to compute two equally spaced numerical solutions for the third-order two point and multipoint boundary value problems (BVPs) s...
Article
Full-text available
This numerical study exclusively focused on the direct two point diagonally multistep block method of order four (2DDM4) in the form of Adams-type formulas. The proposed predictor–corrector scheme was applied in this study to compute two equally spaced numerical solutions for the third-order two point and multipoint boundary value problems (BVPs) s...
Article
Full-text available
Differential equations of fractional order are believed to be more challenging to compute compared to the integer-order differential equations due to its arbitrary properties. This study proposes a multistep method to solve fractional differential equations. The method is derived based on the concept of a third-order Adam–Bashforth numerical scheme...
Article
Full-text available
This paper proposes an implicit block method with two-point to directly solve the fourth-order Initial Value Problems (IVPs). The implicit block method is derived by adopting Hermite interpolating polynomial as the basis function, incorporating the first derivative of f t , y , y ′ , y ′ ′ , y ′ ′ ′ to enhance the solution’s accuracy. A block formu...
Article
Full-text available
Abstract In this paper, we analyze the criteria for the stability of a method suited to the ordinary differential equations models. The relevant proof that the method satisfies the condition of stiff stability is also provided. The aim of this paper is therefore to construct an efficient two-point block method based on backward differentiation form...
Article
Full-text available
The aim of this paper is to solve the initial-value problem for single �first order neutral delay differential equation (NDDE) of constant delay type by applying explicit method. In order to fi�nd the approximate solution of the problem, a two-point explicit multistep block method has been derived by implementing Taylor series interpolation polynom...
Article
Full-text available
In the present paper, a fifth-order direct multistep block method is proposed for solving the second-order Delay Differential Equations (DDEs) directly with boundary conditions using constant step size. In many life sciences applications, a delay plays an essential role in modelling natural phenomena with data simulation. Thus, an efficient numeric...
Article
Full-text available
The initial-value problem for first order single linear neutral delay differential equations (NDDEs) of constant and pantograph delay types have been solved by using hybrid multistep block method. The method has been derived by applying Taylor series interpolation polynomial and implementing the predictor-corrector formulas in mode where is the num...
Article
Full-text available
In this paper, a class of rational methods of second to fourth order of accuracy are presented. The methods are developed by considering the concept of the closest points of approximation in its formulas. These methods require the application of a suitable method to calculate the starting approximation values as they are not self-starting, as well...
Article
Full-text available
This study focuses on the multistep integration method for approximating directly the solutions of the second order boundary value problems (BVPs) with Robin boundary conditions. The derivation of the predictor and corrector formulas uses Lagrange interpolation polynomial in the form of Adam's method. Two numerical solutions are computed concurrent...
Article
Full-text available
This study is intended to evaluate numerically the solution of second order boundary value problems (BVPs) subject to mixed boundary conditions using a direct method. The mixed set of boundary conditions is subsumed under Type 1: mixed boundary conditions of Dirichlet and Robin and Type 2: mixed boundary conditions of Robin and Neumann. The direct...
Article
Full-text available
The hybrid block one-step method of order four is presented and implemented to solve first order Volterra Integro-Differential Equations (VIDEs). The technique is developed using Lagrange interpolation method. The numerical solutions of VIDEs will be solved at two-point concurrently using the proposed numerical method. Properties of the method such...
Article
Full-text available
This study will consider the implementation of direct multistep method for solving Delay Differential Equations (DDEs) with boundary conditions. The approach of this method is solving DDEs directly using the proposed method without reducing to the system of first order. To execute the direct multistep method to solve Boundary Value Problems (BVPs),...
Article
Full-text available
In this paper, we proposed the numerical solution of Volterra integro-differential equations of the second kind using Improved Runge-Kutta method of order three and four with 2 stages and 4 stages, respectively. The improved Runge-kutta method is considered as two-step numerical method for solving the ordinary differential equation part and the int...
Article
Full-text available
In this paper, the numerical solution of delay differential equations using a predictor-corrector scheme in modified block method is presented. In this developed algorithm, each coefficient in the predictor and corrector formula are recalculated when the step size changing. The Runge-Kutta Fehlberg step size strategy has been applied in the algorit...
Article
Full-text available
In this paper, we proposed to deal with the derivative discontinuities in the numerical solution of functional differential equation by using the technique of discontinuity tracking equations. This technique will be adapted in a linear multistep method with the support of Runge-Kutta Felhberg step size strategy. Naturally, the existence of disconti...
Article
Full-text available
A direct explicit Runge-Kutta type (RKT) method via shooting technique to approximate analytical solutions to the third-order two-point boundary value problems (BVPs) with boundary condition type I and II are proposed. In this paper first, a three-stage fourth-order direct explicit Runge-Kutta type method denoted as RKT3s4 is constructed. A new alg...
Article
Full-text available
In this paper, a fuzzy general linear method of order three for solving fuzzy Volterra integro-differential equations of second kind is proposed. The general linear method is operated using the both internal stages of Runge-Kutta method and multivalues of a multisteps method. The derivation of general linear method is based on the theory of B-serie...
Book
Full-text available
This book is the first volume of research papers presented at the Fundamental Science Congress 2017 at Universiti Putra Malaysia on November 21-22, 2017.The congress served as a platform for researchers from different parts of Malaysia to share their knowledge and initiate collaboration among themselves. This book presents the latest findings in va...
Article
Full-text available
This numerical study presents the diagonal block method of order four for solving the second-order boundary value problems (BVPs) with Robin boundary conditions at two-point concurrently using constant step size. The solution is obtained directly without reducing to a system of first-order differential equations using a combination of predictor-cor...
Article
Full-text available
In this paper, we proposed a fifth-order Runge-Kutta (RK) technique for regulating coordination about third-order ordinary differential equations (ODEs) of the structure y′′′ = f(x, y, y′) indicated similarly as RKTG method is constructed. The order state about RKTG method up to order six were proved and verified. In view of those order conditions...
Conference Paper
Full-text available
This paper presents novel mixed multistep block methods for the solution of second-order Ordinary Differential Equations (ODEs) using variable step size approach. The approach employs on the combination of Block Backward Differentiation Formulas (BBDF) and block of Adams type formulas. The theory of each method is discussed for the derivation of th...
Article
Full-text available
In this study, a five-stage fourth-order Runge-Kutta type method for directly solving general third-order ordinary differential equations (ODEs) of the form y''' = f (x, y, y', y'') which is denoted as RKTGG method is constructed. The order conditions of RKTGG method up to order four are derived. Based on the order conditions developed, five-stage...
Article
Full-text available
The effects of temperature dependent viscosity and internal heat generation on the onset of steady Bénard-Marangoni convection in a horizontal binary fluid layer heated from below is investigated theoretically. The upper free surface is assumed to be deformable and the lower boundary is considered to be rigid and perfectly insulated to temperature...
Article
Full-text available
In this paper, the solution of fuzzy differential equations is approximated numerically using diagonally implicit multistep block method of order four. The multistep block method is well known as an efficient and accurate method for solving ordinary differential equations, hence in this paper the method will be used to solve the fuzzy initial value...
Article
Full-text available
The performance of the numerical computation based on the diagonally implicit multistep block method for solving Volterra integrodifferential equations (VIDE) of the second kind has been analyzed. The numerical solutions of VIDE will be computed at two points concurrently using the proposed numerical method and executed in the predictor-corrector (...
Chapter
Full-text available
The numerical solution of the second kind of Volterra integro-differential equation (VIDE) implementation of the implicit multistep block method is discussed in this paper. This method will approximate the solutions for the ordinary differential equation part of the VIDE at two points simultaneously using constant step size. The appropriate quadrat...
Article
In this paper, a predictor corrector two-point block method is proposed to solve the well-know Blasius and Sakiadis flow numerically. The Blasius and Sakiadis flow will be modeled by a third order boundary value problem. The main motivation of this study is to provide a new method that can solve the higher order BVP directly without reducing it to...
Article
Full-text available
Finding accurate and efficient methods for solving nonlinear hyper chaotic problems has long been an active research undertaking. Like the well-known Adomian decomposition method (ADM) and based on observations, it is hopeless to find HPM solutions of hyper chaotic systems valid globally in time. To overcome this shortcoming, we employ the multista...
Conference Paper
Temperature dependent viscosity and Coriolis force were applied to the steady Benard-Marangoni convection where the lower boundary of a horizontal layer of the binary mixture is heated from below and cooled from above. The purpose of this paper is to study in detail the onset of convection with these effects. Few cases of boundary conditions are st...
Article
Full-text available
This paper outlines an alternative algorithm for solving general second order ordinary differential equations (ODEs). Normally, the numerical method was designed for solving higher order ODEs by converting it into an n-dimensional first order equations with implementation of constant step length. Nevertheless, this involved a lot of computational c...
Article
Full-text available
In this research, the quadrature-difference method with Gauss Elimination (GE) method is applied for solving the second-order of linear Fredholm integrodifferential equations (LFIDEs). In order to derive an approximation equation, the combinations of Composite Simpson’s 1/3 rule and second-order finite-difference method are used to discretize the s...
Article
Full-text available
In this paper, the two-point direct block method with one-off step is considered for solving boundary value problems (BVPs) with Dirichlet boundary conditions. The direct block method with one-off step is of type one-step method where it needs only one-point to start the next block. This method solves the second order BVPs directly without reducing...
Article
Thermosolutal Rayleigh-Benard convection in a binary fluid heated from the below is studied numerically. Soret effects are imposed to analyze the thermo-diffusion effects on the flow. We study the onset of convection in a horizontal binary fluid layer with the effect of temperature dependent viscosity together with vertical magnetic field. The conf...
Article
Full-text available
This study has constructed an explicit Trigonometrically-Fitted Modified Runge-Kutta (TFMRK) method for solving first-order differential equations with periodic solutions. The newly developed method was made according to the method of Runge-Kutta Dormand and to fourth algebraic order. Numerical results for the new method were compared with the exis...
Conference Paper
This paper presents a four point block one-step method for solving directly boundary value problems (BVP) with Neumann boundary conditions and Singular Perturnbation BVPs. This method is formulated using Lagrange interpolating polynomial. The block method will solve the second order linear Neumann and Singular Perturbation BVPs directly without red...
Article
Full-text available
In this paper, an explicit embedded pair Runge-Kutta (RK) method which is denoted by TFRKF6(5) is developed to determine the approximate solution of the first-order IVPs with oscillatory solution. The proposed method solves first order ODEs by first converting higher order ODEs to an equivalent first order system. This embedded scheme has algebraic...
Article
Full-text available
A fourth order diagonally implicit multistep block method is introduced to approximate the solution of fuzzy differential equations (FDEs). The problem is interpreted by using Seikkala's derivative. This method approximates two points simultaneously in a block along the interval. The Lagrange interpolating polynomial is applied in the formation of...
Article
Full-text available
In this paper, we use multistep block method for solving linear and non-linear Volterra integro-differential equations (VIDEs) of the second kind. The VIDEs will be solved by using the combination of multistep block method of order three and Newton-Cotes quadrature rule of suitable order. The proposed method will solve VIDEs for K(x, s) = 1 and K(x...
Article
Full-text available
In this work, a new way for constructing an efficiently modified Runge-Kutta (RK) method to solve first-order ordinary differential equations with oscillatory solutions is provided. The proposed method solves the first-order ODEs by first converting the second order ODEs to an equivalent first-order ODEs. The method of the embedded has algebraic or...
Article
In this paper, we propose an A-stable one-step block method of order four for solving a stiff ordinary differential equation. This method will approximate the solutions of a stiff ordinary differential equation at three points simultaneously using a constant step size. The method is similar to the one-step method and it is self-starting but the imp...
Conference Paper
Full-text available
In this note, an explicit trigonometrically-fitted (RK) method is developed to determine the approximate solution of the first-order IVPs with oscillatory solution. The proposed method solves first order ODEs by first converting the second order ODEs to an equivalent first order; which is based on the RK method of order four. The numerical experime...
Chapter
In this paper, a self-starting one-step implicit hybrid method is proposed to solve semi-explicit index-1 differential algebraic equations (DAEs). The proposed method is formulated using Lagrange interpolating polynomial. The proposed method will compute the solutions of differential algebraic equations using constant step size. Implementation of t...
Article
Full-text available
A new Runge-Kutta (RK) method is constructed to solve first-order differential equations with oscillatory solutions. This new method is based on the Runge-Kutta method of order four with seven-stage. Numerical tests are performed, and the results of the new method is compared with the existing methods. The numerical results show that the new method...
Article
Full-text available
In this paper, a new phase-fitted and amplification-fitted modified Runge-Kutta (MRK) method is constructed to solve first-order ordinary differential equations with oscillatory solutions. This new method is based on the Runge-Kutta Zonneveld method with fourth algebraic order. The numerical results for the new method have been compared with other...
Article
Full-text available
An alternative block method for solving fifth-order initial value problems (IVPs) is proposed with an adaptive strategy of implementing variable step size. The derived method is designed to compute four solutions simultaneously without reducing the problem to a system of first-order IVPs. To validate the proposed method, the consistency and zero st...
Book
This book features selected papers from The Seventh International Conference on Research and Education in Mathematics that was held in Kuala Lumpur, Malaysia from 25 - 27th August 2015. With chapters devoted to the most recent discoveries in mathematics and statistics and serve as a platform for knowledge and information exchange between experts fr...
Conference Paper
Full-text available
One-step block method for solving linear Volterra integro-differential equations (VIDEs) is presented in this paper. In VIDEs, the unknown function appears in the form of derivative and under the integral sign. The popular methods for solving VIDEs are the method of quadrature or quadrature method combined with numerical method. The proposed block...
Conference Paper
Full-text available
In this paper, an implicit multistep block method of order three is proposed for solving fuzzy differential equations. The method is based on diagonally implicit multistep block method where the coefficients of the lower triangular matrix entries are zero. This method works by moving two steps in a block, thus the values of y n+1 and y n+2 are ap...
Conference Paper
Full-text available
In this paper, a self-starting block method of Runge Kutta type is proposed to solve semi-explicit index-1 differential algebraic equation (DAE). Semi-explicit DAE consists of a system of ordinary differential equations with algebraic constraints. This method will compute the solutions of DAE at two points simultaneously in a block by block steps u...
Article
Full-text available
This paper will consider the implementation of direct two-point fourth and fifth order multistep block method in the form of Adams–Moulton method to solve second order delay differential equations (DDEs) directly without transforming the equations into system of first order DDEs. The proposed methods will compute the numerical solutions at two poin...
Conference Paper
Full-text available
A new Runge-Kutta method, with phase-fitted and amplification-fitted is constructed for solving first-order ordinary differential equations with periodic solutions. This new method is based on the Runge-Kutta 3/8 Rule with fourth algebraic order. In the numerical results the new method is compared with the existing method; which show that the new m...
Conference Paper
Full-text available
In this paper, a variable step size and variable order strategy ( VSVO) used in the block method is developed for solving directly the second order two-point boundary value problems (BVPs). The variable step size and variable order strategy managed to reduce the total step and assure the accuracy of the method. The proposed block method can compute...
Conference Paper
Full-text available
This paper presents 4-point 1-step block method (4LBVP) to solve the linear 2nd order boundary value problem (BVP) with Dirichlet boundary condition. 4LBVP will solve the linear 2nd order BVP with Dirichlet boundary condition directly without the need to reduce it first into the system of 1st order equations. 4LBVP will produce several numerical so...
Conference Paper
Full-text available
The purpose of this paper is to solve directly the second order delay differential equations (DDEs) using The extended two and extended three point implicit one-step block methods using constant step size. The formulae for the extended two and extended three point implicit one-step block methods will be derived using Lagrange interpolation polynomi...
Conference Paper
Full-text available
Modeling of certain complex problems in science and engineering involve fuzzy differential equations. Many fuzzy differential equations cannot be solved analytically because of the complexity of the modeled problems. In this paper, a multistep block method is proposed for numerically solving first order fuzzy differential equations using Hukuhara d...
Conference Paper
Full-text available
This paper will implement the use of two-point block method in the form of predictor-corrector Adams-Moulton to solve first order neutral delay differential equations (NDDES) of pantograph type. This two-point block method will compute the numerical solution at two points simultaneously. This method will approximate the solutions using constant ste...
Conference Paper
A new Runge-Kutta method, with phase-fitted and amplification-fitted is constructed for solving first-order ordinary differential equations with periodic solutions. This new method is based on the Runge-Kutta 3/8 Rule with fourth algebraic order. In the numerical results the new method is compared with the existing method; which show that the new m...
Conference Paper
Full-text available
A 2-point diagonally implicit multistep block method of order five is proposed. It is implemented to find the approximation for first-order fuzzy differential equations (FDEs) under on Seikkala derivative. This block method operates by approximating two points at yn+1 and yn+2 concurrently in a step. Both formulas are derived by using Lagrange inte...
Conference Paper
Full-text available
Application of the quadrature-difference method for solving Fredholm integro-differential equations (FIDEs) is presented in this paper. The FIDEs will be discretized by using the combinations of Simpsons quadrature rule with finite difference. The method converts the FIDEs to a matrix equation which corresponds to a system of linear algebraic equat...
Conference Paper
Full-text available
An extended 2-point one-step block method formula with order four is formulated for solving stiff initial value problem. The method is similar to Runge-Kutta method which has a self-starting formula. The approximation solutions at two points will be computed simultaneously by integrating the coefficients over the closest point in the block. The acc...
Article
Full-text available
The recent convergence outcomes of faster group iterative schemes from the Modified Successive Over-Relaxation (MSOR) family have initiated considerable attention in reconnoitering the comportment of these methods in the solution of partial differential equations (PDEs). In 2011, Akhir et al., [12] formulated a new four Point-Explicit Group MSOR (E...
Conference Paper
In this paper, the fourth order predictor-corrector method in the form of linear multistep method will be presented to solve delay differential equations of pantograph type. This special type of delay differential equations always has the delay term fall after the initial value but before the desire approximation being calculated. The new approach...
Conference Paper
In this paper, we propose an algorithm of two-point block method to solve the nonlinear system of third-order boundary value problems directly. The proposed method is presented in a simple form of Adams type and two approximate solutions will be obtained simultaneously with the block method using variable step size strategy. The method will be impl...
Conference Paper
This article presents a technique on how to deal with the presence of small delay case in delay differential equations. This case has been classified as one of the difficulties in the numerical solution where it is due to the delay value that is smaller than the current step size and there is no current approximate solution that can be used in the...
Article
Full-text available
The multistep block method is applied to solve the particular vanishing delay case in delay differential equations. The proposed method which is based on predictor-corrector scheme are used to determine three approximate solutions concurrently in each step of integration. The new strategy to obtain the solution of the vanishing delay within the thr...
Article
Full-text available
A fifth order block method of Adam's type is presented to obtain the numerical solution of the boundary layer problem. The boundary layer problem we handle in this research is nanofluid over a moving surface in a flowing fluid. It is modelled as a system of combination of third order and second order differential equations subject to the two point...
Article
Full-text available
In this paper, we discussed and compared the computational complexity for two-point block method and one-point method of Adams type. The computational complexity for both methods is determined based on the number of arithmetic operations performed and expressed in O(n). These two methods will be used to solve two-point second order boundary value p...

Network

Cited By