# Adibi HojatollahAmirkabir University of Technology | TUS · Applid Mathemativs

Adibi Hojatollah

Doctor of Philosophy

## About

75

Publications

15,857

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

1,045

Citations

Citations since 2016

## Publications

Publications (75)

This paper develops an efficient numerical meshless method to solve the nonlinear generalized Burgers–Huxley equation (NGB-HE). The proposed method approximates the unknown solution in the two stages. First, the θ-weighted finite difference technique is adopted to discretize the temporal dimension. Second, a combination of the multiquadric quasi-in...

This study documents the development of a novel scheme for spatial discretization of the time-fractional Sobolev equation. The scheme is based on a combination of continuous and discontinuous Galerkin methods which is called the enriched Galerkin method. The enriched Galerkin method has more degrees of freedom than the continuous Galerkin but small...

In this article, an efficient method for approximating the solution of the generalized
Burgers-Huxley (gB-H) equation using multiquadric quasi-interpolation approach
is considered. This method consists of two phases. First the spatial derivatives are
evaluated by MQ quasi-interpolation, So the gB-H equation is reduced to a nonlinear
system of ordin...

In this paper, the Laplace transform combined with the local discontinuous Galerkin method is used for distributed‐order time‐fractional diffusion‐wave equation. In this method, at first, we convert the equation to some time‐independent problems by Laplace transform. Then, we solve these stationary equations by the local discontinuous Galerkin meth...

In this paper, Spectral Galerkin Method (SGM) is applied for Cauchy problem of Helmholtz
and Laplace equations in the regular domains. It is well known that these problems have severely ill-
posed solutions. Accordingly, regularization methods are required to overcome the ill-posedness issue. In
this paper we utilize the regularization method based...

در این مقاله، معادله لاپلاس تحت شرایط مرزی دیریکله و کوشی به دو روش عددی
مختلف حل میشود. ابتدا مسئله کوشی معادله لاپلاس به روش گالرکین طیفی حل
میشوداز آنجا که این مسئله بدوضع است به منظمسازی مقادیر ویژه آن پرداخته
میشود و در ادامه، معادله لاپلاس با شرایط مرزی دیریکله به وسیله یک روش
تکراری تفاضلات متناهی حل میگردد. در بخش پایانی این دو روش برای مسئ...

خلاصه
در این مقاله، روش تفاضلات متناهی برای معادله موج دوبعدی در یک دامنه
مستطیلی شکل با شرایط اولیه و مرزی به کار برده میشود. پایداری روش
استفاده شده مورد بررسی قرار میگیرد و با چند مثال عددی میزان موثر بودن
روش نشان داده میشود.

This paper presents a numerical solution of time-fractional nonlinear advection–diffusion equations (TFADEs) based on the local discontinuous Galerkin method. The trapezoidal quadrature scheme (TQS) for the fractional order part of TFADEs is investigated. In TQS, the fractional derivative is replaced by the Volterra integral equation which is compu...

Purpose
This paper aims to propose an adaptive method for the numerical solution of the shallow water equations (SWEs). The authors provide an arbitrary high-order method using high-order spline wavelets. Furthermore, they use a non-linear shock capturing (SC) diffusion which removes the necessity of post-processing.
Design/methodology/approach...

This paper deals with exact soliton solutions of the nonlinear long–short wave interaction system, utilizing two analytical methods. The system of coupled long–short wave interaction equations is investigated with the help of two analytical methods, namely, the generalized \(\tan (\phi /2)\)-expansion method and He’s semi-inverse variational method...

In this study, the generalized \(\tan (\phi /2)\)-expansion method and He’s semi-inverse variational method (HSIVM) are applied to seek the exact solitary wave solutions for the resonant nonlinear Schrödinger equation with time-dependent coefficients. Using these methods, we investigate exact solutions for the nonlinear resonant Schrödinger equatio...

This article concerns with incorporating wavelet bases into existing streamline upwind Petrov-Galerkin (SUPG) methods for the numerical solution of nonlinear hyperbolic conservation laws which are known to develop shock solutions. Here, we utilize an SUPG formulation using continuous Galerkin in space and discontinuous Galerkin in time. The main mo...

In this paper, we extend the application of meshfree node based schemes for solving one-dimensional inverse Cauchy-Stefan problem. The aim is devoted to recover the initial and boundary conditions from some Cauchy data lying on the admissible curve s(t) as the extra overspecifications. To keep matters simple, the problem has been considered in one...

This paper is concerned with giving a simple mathematical model on the propagation of longitudinal stress waves in a Voigt viscoelastic porous media. This model is congruent with the Frankel-Biot theory and describes the differences between vibrations of solid and liquid parts of porous medium. Furthermore, this model shows that there is a critical...

In this paper, we present a meshless method of lines to solve one-dimensional advection–diffusion equation. For this aim, we use radial basis functions for approximate derivatives in space and fourth order Runge–Kutta scheme to solve the gained system of ordinary differential equations. Here, we use different types of radial basis functions such as...

In this paper, we are concerned with the numerical solutions of the inverse heat conduction problems (IHCP) in one and two dimensions with free boundary conditions. For the one-dimensional problem, we first apply the Landau’s transformation to replace the physical domain with a rectangular one. Reciprocally, some nonlinear terms appear thus an iter...

In this study we propose a hybrid spectral exponential Chebyshev method (HSECM) for solving time-fractional coupled Burgers equations (TFCBEs). The method is based upon a spectral collection method, utilizing exponential Chebyshev functions in space and trapezoidal quadrature formula (TQF), and also a finite difference method (FDM) for time-fractio...

This paper is concerned with the numerical solution of the time fractional coupled Burgers’ equation. The proposed hybrid solution is based on Chebyshev collection method for space variable, and the trapezoidal quadrature technique. Finally the error analysis is discussed and some test examples are presented to demonstrate the applicability and eff...

In this paper, we present a numerical method proficient for solving a system of time–fractional partial differential equations. For this sake, we use spectral collection method based on shifted Chebyshev polynomials in space and finite difference method for time fractional derivative. Furthermore, we employ this method to solve the time-fractional...

در اين مقاله، روش هم مکانی توابع پایه¬ای شعاعی را به عنوان یک روش بدون شبکه برای حل عددی معادلات با مشتقات جزئی شرح می-دهیم. درونیابی به وسیله¬ی توابع پایه¬ای شعاعی، فرایند حل معادلات مستقل از زمان و یکی از رویکردهای مبتنی بر توابع پایه¬ای شعاعی برای حل معادلات وابسته به زمان را بیان می¬کنیم. در رویکرد یاد شده، برای حل معادلات وابسته به زمان، ابتدا...

در اين مقاله يك روش عددي مبتني بر توابع پايهاي شعاعي، براي حل معادله ي خطي مرتبه دوم دو بعدي تلگراف ارائه مي كنيم. ابتدا توابع پايه اي شعاعي را معرفي كرده و حل معادله دو بعدي تلگراف با توابع پايه اي شعاعي را مورد بررســي قــرار خــواهيم داد. در روش پيشــنهاد شــده ابتــدا معادله ي تلگراف را با يك روش تفاضلات متناهي (كرانك – نيكلسون) گسسته سازي كرده...

This paper presents two numerical solutions of time fractional Fokker-Planck equations (TFFPE) based on the local discontinuous Galerkin method. Two time–discretization schemes for the fractional order part of TFFPE are investigated. The first discretization utilizes the fractional finite difference scheme (FFDS) and in the second scheme the fracti...

In this paper a modification of the Legendre collocation method is applied to the solution of space fractional differential equations. The fractional derivative is considered in the Caputo sense. The finite difference scheme and Legendre collocation method are used. The numerical results obtained by this way have been compared with other methods. T...

In this note, we apply a numerical method to solve viscoelastic models involving fractional derivatives. Our method generalizes rational Legendre collocation scheme. It uses new functions named "fractional rational Legendre functions" as the basis. The new basis convergence more rapidly than rational Legendre functions in solving fractional differe...

In this paper, we propose a new scheme that combines weighted essentially non-oscillatory (WENO) procedures together with monotone upwind schemes to approximate the viscosity solution of the Hamilton–Jacobi equations. In one-dimensional (1D) case, first, we obtain an optimum polynomial on a four-point stencil. This optimum polynomial is third-order...

In this article, we discuss the application of two important numerical methods, Ritz–Galerkin and Method of Fundamental Solutions (MFS), for solving some inverse problems, arising in the context of two-dimensional elliptic equations. The main incentive for studying the considered problems is their wide applications in engineering fields. In the pre...

In this paper numerical meshless method for solving Fokker–Planck equation is considered. This meshless method is based on multiquadric radial basis function and collocation method to approximate the solution. Here we apply θ-weighted finite difference method. The stability analysis of the method is dealt with, using a linearized stability method....

Propagation of mechanical waves’ phenomenon is the result of infinitely small displacements of integrated individual particles in the materials. These displacements are governed by Navier-Lame and Navier-Stokes equations in solids and fluids, respectively. In the present work, a generalized Kelvin-Voigt model of viscoelasticity has been proposed wi...

In this article, our main goal is to render an idea to convert a nonlinear weakly singular Volterra integral equation to a non-singular one by new fractional-order Legendre functions. The fractional-order Legendre functions are generated by change of variable on well-known shifted Legendre polynomials. We consider a general form of singular Volterr...

Three inverse problems of reconstructing the time-dependent, spacewise- dependent and both initial condition and spacewise-dependent heat source in the one-dimensional heat equation are considered. These problems are reformulated by eliminating the unknown functions using some special assumptions concerning the points in space or time as additional...

This paper investigates a numerical method for solving two-dimensional
nonlinear Fredholm integral equations of the second kind on non-rectangular
domains. The scheme utilizes the shape functions of the moving least squares (MLS)
approximation constructed on scattered points as a basis in the discrete collocation
method. The MLS methodology is an e...

This paper describes a computational method for solving Fredholm integral equations of the second kind with logarithmic kernels. The method is based on the discrete Galerkin method with the shape functions of the moving least squares (MLS) approximation constructed on scattered points as basis. The MLS methodology is an effective technique for the...

This article investigates a numerical scheme based on the radial basis functions (RBFs) for solving weakly singular Fredholm integral equations by combining the product integration and collocation methods. A set of scattered points over the domain of integration is utilized to approximate the unknown function by using the RBFs. Since the proposed s...

This paper describes a numerical scheme based on the Chebyshev wavelets constructed on the unit
interval and the Galerkin method for solving nonlinear Fredholm-Hammerstein integral equations of the
second kind. Chebyshev wavelets, as very well localized functions, are considerably effective to estimate
an unknown function. The integrals included in...

This work is motivated by studies of numerical simulation for solving the inverse one and two-phase Stefan problem. The aim is devoted to employ two special interpolation techniques to obtain space-time approximate solution for temperature distribution on irregular domains, as well as for the reconstruction of the functions describing the temperatu...

In this paper, we propose a new weighted essentially non-oscillatory (WENO) procedure for solving hyperbolic conservation laws, on uniform meshes. The new scheme combines essentially non-oscillatory (ENO) reconstructions together with monotone upwind schemes for scalar conservation laws’ interpolants. In a one-dimensional context, first, we obtain...

In this paper, we present a computational method for solving boundary integral
equations with logarithmic singular kernels which occur as reformulations of a boundary value
problem for Laplace's equation. The method is based on the use of the Galerkin method
with CAS wavelets constructed on the unit interval as basis. This approach utilizes the non...

In this paper, a generalization of rational Chebyshev functions and named fractional rational Chebyshev functions, is introduced for solving fractional differential equations. By using the collocation scheme, the efficiency and performance of the new basis is shown through several examples. Also, the obtained results are compared with rational Cheb...

The main purpose of this article is to describe a numerical scheme for solving two-dimensional
linear Fredholm integral equations of the second kind on a non-rectangular domain.
The method approximates the solution by the discrete collocation method based on radial
basis functions (RBFs) constructed on a set of disordered data. The proposed method...

In this paper, we propose a new WENO finite difference procedure for nonlinear degenerate parabolic equations which may contain discontinuous solutions. Our scheme is based on the method of lines, with a high-order accurate conservative approximation to each of the diffusion terms based on an idea that has been recently presented by Liu et al. [Y....

An inverse problem for the determination of the unknown spacewise-dependent coefficients in a hyperbolic equation through additional boundary measurements is considered. For the sake of simplicity, the problem has been considered in one dimension, however the method is applicable for problems with regular and bounded domains in higher dimensions. T...

This article describes a numerical method based on the boundary integral equation and dual reciprocity method(DRM) for solving the one-dimensional advection-diffusion equations. The concept of DRM is used to convert the domain integral to the boundary that leads to an integration free method. The time derivative is approximated by the time-stepping...

In this paper, we present a numerical method for solving two-dimensional nonlinear Fredholm integral equations of the second kind on a non-rectangular domain. The method utilizes radial basis functions (RBFs) constructed on scattered points as a basis in the discrete collocation method. The proposed scheme is meshless, since it does not need any do...

In this paper, we present a computational method
for solving Fredholm-Hammerstein integral equations of the second
kind. The method utilizes shape functions of the moving least
squares (MLS) approximation constructed on scattered points as a
basis in the discrete collocation method. The MLS methodology is
an effective technique for the approximatio...

This paper describes a numerical method for solving nonlinear mixed Volterra-Fredholm
type integral equations of the second kind. The proposed method utilizes radial basis functions (RBFs)
with polynomial precision as a basis in the discrete collocation method. The RBF technique is an
effective scheme for the approximation of an unknown function us...

In this paper, a new method is applied to deal with domain integrals of boundary element method (BEM). In fact we focus to convert the domain integrals into boundary integrals for non-homogenous Laplace, Helmholtz and advection diffusion equations in two dimensional BEM. The transformation presented in this paper is based on divergence theorem. In...

Purpose
– The purpose of this work is to analytically examine the magnetohydrodynamic (MHD) Falkner‐Skan flow.
Design/methodology/approach
– The series solution is obtained using the Adomian decomposition method (ADM) coupled with Padé approximants.
Findings
– Comparison of the present solutions is made with the results obtained by other applied...

In this paper, we present a numerical method for solving, linear and nonlinear, weakly singular Fredholm integral equations of the second kind. The method utilizes Legendre wavelets constructed on the unit interval as a basis in the Galerkin method and reduces the solution of the Fredholm integral equation to the solution of a system of algebraic e...

This paper is concerned with the construction of a biorthogonal multiwavelet basis in the unit interval to form a biorthogonal flatlet multiwavelet system. The system is then used to solve nonlinear ordinary differential equations. The biorthogonality and high vanishing moment properties of this system result in efficient and accurate solutions. Fi...

In this paper, approximate solutions of singular initial value problems (IVPs) of the Lane–Emden type in second-order ordinary differential equations (ODEs) are obtained by an improved Legendre-spectral method. The Legendre–Gauss points are used as collocation nodes and Lagrange interpolation is employed in the Volterra term. The results reveal tha...

Smoluchowski's equation is widely applied to describe the time evolution of the cluster-size distribution during aggregation processes. Analytical solutions for this equation, however, are known only for a very limited number of kernels. Therefore, numerical methods have to be used to describe the time evolution of the cluster-size distribution. A...

Special type of linear Fredholm integro-differential equations is considered. In this research, two analytical methods, called homotopy-perturbation method (HPM) and variational iteration method (VIM) and one numerical method, finite difference method are used for solving these equations. The results of applying these methods to the linear integro-...

In this paper, an application of Legendre-spectral method is applied to solve functional integral equations. The Legendre Gauss points are used as collocation nodes and Lagrange scheme is employed to interpolate the quantities needed. Using this approach a generalized functional integral equation both linear and nonlinear could be considered. The m...

This paper studies a class of nonlinear second order difference equations of the type xn+1=f(xn, xn-1/xn), where f is symmetric and monotonic with initial conditions x-1,x 0 being positive real numbers. Some sufficient conditions under which every positive solution of such equation converges to a period two solution or to the cycle {0,∞} are establ...

This paper is concerned with the construction of biorthogonal multi-wavelet basis in the unit interval to form a biorthogonal flatlet multiwavelet system. Next a method to calculating derivatives of the dual flatlet multiwavelets by multiplying some matrices is suggested. The system is then used to integro-differential equations. The biorthogonalit...

A computational method for solving Fredholm integral equations of the first kind is presented. The method utilizes Chebyshev wavelets constructed on the unit interval as basis in Galerkin method and reduces solving the integral equation to solving a system of algebraic equations. The properties of Chebyshev wavelets are used to make the wavelet coe...

In this paper, we present a computational method for solving Volterra integral equations of the second kind which is based on the use of CAS wavelets. The operational matrix of integration (OMI) and the product operation matrix (POM) for CAS wavelets are introduced and used to reduce solving the Volterra integral equation to solving a system of alg...

The general solution, the local and global asymptotic stability of equilibrium points and period three cycles of the third order rational difference equationare studied in this paper.

In this paper, we consider complete Hyper Menger probabilistic quasi-metric space and prove some fixed point theorems in this space.

In this paper we construct a flatlet biorthogonal multiwavelets System. Then, we use this system for numerical solution of Integro-differential equations. The good prop-erties of this system, i.e., biorthogonality and more vanishing moments lead to efficient and accurate solutions. Some test problems with known solutions are presented and the numer...

In this paper, a common fixed point theorem for commuting maps in L-fuzzy metric spaces is proved.

Biharmonic equation has significant applications in physics and engineering, but is difficult to solve due to the existing fourth order derivatives. One of the domain-type mashless methods is obtained by simply applying the radial basis functions (RBFs) as a direct collocation, which has shown to be effective in solving complicated physical problem...

An effective numerical method is developed in this paper for the Laplace equation as one of the most significant equations of physics and engineering. Our approach based on Chebyshev Tau technique utilizes Chebyshev polynomials and the associated operational matrix of derivative. Illustrative examples are included and numerical results obtained via...

In this paper, at first we prove a common fixed point theorem in L-fuzzy metric space. Secondly, to introduce the concept of compatible mappings of type (P) in L-fuzzy metric space, which is equivalent to the concept of compatible and compatible mappings of type (A) under some appropriate conditions. In the sequel, we derive some relations between...

We show that Theorem 2.4 of a recent paper by I.H. Jebril and R.I.M. Ali is incor- rect.

We consider finite-dimensional intuitionistic fuzzy normed spaces. We prove some theorems about complete normed spaces, compact normed spaces and weak convergence in finite-dimensional intuitionistic fuzzy normed spaces.

## Questions

Question (1)

To whom it may concern,

Despite receiving several notification emails from the research gate, about the new citation of my paper titled:

Convergence criteria for a class of second-order difference equations , by H Adibi, Xinzhi Liu, M Shojaei, , unfortunately its citation# is still 1.

I would appreciate if you would let me know why is this so?

Best regards,

Prof. H Adibi

Department of Applied Mathematics,
Faculty of Mathematics and Computer Sciences,
Amirkabir University of Technology,
424 Hafez Avenue,
P.O. Box 15875-4413,

Tehran,
Iran

Tel: +98 21 22802217

## Projects

Projects (2)

My main goal in the first project is to study the effect of matrix viscoelasticity on the behaviour of stress waves propagation, and in second project I define some hybrid numerical methods and I want to compare these method by exists methods.