Mohammad Al-Towaiq

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Mohammad verified their affiliation via an institutional email.

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• PhD
• Professor at Jordan University of Science and Technology

Initial-value problems (IVP) of ordinary differential equations modeling many physical phenomena in applied science and engineering. We consider the following IVP for ordinary differential equations ′ () = (, ()), (0) = 0 (1) This type of equations often has a difficulty to find an analytical solution because most of them are nonlinear. Therefore,...

In this paper, we present parallel implementations of the Gauss-Jordan and Gauss-Huard algorithms with scaled partial pivoting strategy on a cluster of Linux workstations using MPI as a parallel programming environment. We present a comparative study of their performance. The obtained experimental results for the test problems and the analysis of t...

In this paper, we propose an efficient modification of the Collocation method which uses a radial basis function (RBF) as a basis function to find an approximate solution of a boundary value problem. We use the Fisher equation as a case study to examine the validity and applicability of the proposed technique. The numerical results show that the pr...

In this paper, we introduce a modified algorithm for the Clenshaw-Curtis (CC) quadrature formula. The coefficients of the formula are approximated by using a finite linear combination of Legendre polynomials in the Least Squares sense to make the CC method well disposed for numerical solution of the definite integral. We design and analyze the modi...

In this paper, a modified algorithm is proposed for solving linear integro- differential equations of the second kind. The main idea is based on applying Romberg extrapolation algorithm (REA), on Trapezoidal rule. In accordance with the computational perspective, the comparison has shown that Adomian decomposition approach is more effective to be u...

In this paper, we propose two efficient extensions classes based on Broyden’s methods and Broyden’s central finite difference for solving systems of nonlinear equations; used to increase order convergence of Broyden’s method. These simple extensions have more accuracy than the basic Broyden’s method. Some numerical examples are given to test the va...

In this paper, two improved methods for Quasi Newton's method (QN) called Quasi Modified Newton's (QMN) of type 1 and type 2, to obtain an approximate solution for systems of nonlinear equations. The most significant features of these methods are their simplicity and excellent accuracy. Error estimation of the methods was discussed. Some numerical...

In this paper, we propose two efficient algorithms based on Broyden's methods using the central finite difference and modification of Newton's method for solving systems of nonlinear equations. The most significant features of these algorithms are their simplicity and excellent accuracy. Some numerical examples are given to test the validity of the...

In this study, two improved methods for Quasi Newton's method (QN) called Quasi Modified Newton's (QMN) of type 1 and 2, to obtain an approximate solution for systems of nonlinear equations. The most significant features of these methods are their simplicity and excellent accuracy. Error estimation of the methods was discussed. Some numerical examp...

Network-on-chip (NoC) multi-core architectures with a large number of processing elements are becoming a reality with the recent developments in technology. In these modern systems the processing elements are interconnected with regular NoC topologies such as meshes and tori. In this paper we propose a parallel Gauss-Seidel (GS) iterative algorithm...

In this paper, we propose an algorithm using the cubic spline interpolation on the finite difference method to solve the Bratu-type equation. The algorithm has been successfully implemented. Numerical results are also given to demonstrate the validity and the applicability of the proposed algorithm. The results we obtained show that the proposed al...

In this paper, we expand the scope of application of the modified variational iteration method (MVIM) to solve the Impenetrable Agar Model Problem. This model represents the propagation of a bacterial exo-enzyme within an impenetrable host material which simulates the manifestations bacteria do on tissue wounds in an infection. The numerical result...

Network-on-chip multicore architectures with a large number of processing elements are becoming a reality with the recent developments in technology. In these modern systems the processing elements are interconnected with regular network-on-chip (NoC) topologies such as meshes and trees. In this paper we propose a parallel Gauss-Seidel (GS) iterati...

In this paper, we present parallel implementation of the Gauss-Seidel (GS) iterative algorithm for the solution of linear systems of equations on a k-ary n-cube parallel machine using Open MPI as a parallel programming environment. The proposed algorithm is of O(N 3 /k n) computational complexity and uses O(nN) communication time to decompose a mat...

In this paper, we develop, analyze, and evaluate a parallel algorithm for diagonally explicit Runge-Kutta method of order four (DERK4) for solving systems of differential equations. A timing model has been developed and verified to estimate the execution time of the proposed algorithm. We used the proposed algorithm to solve a predator-prey system...

In this paper, we propose an adaptive mathematical model for the three species: nutrient, algae, and small fish predator-prey system. We formulate the model for the system, investigate sufficient conditions for the existence of positive periodic solutions, and checking the validity of the model. Then we study the stability, and asymptotical behavio...

Taylor expansion method for the solution of second order PDE’s, is based on taking truncated Taylor polynomial about any point of the coefficients functions has been investigated by Kesan [3]. In this paper, we develop an algorithm for the solution of the PDE’s of the form f (x, y) uxx – g (x, y) uyy = h (x, y), with any boundary conditions, based...

Huffman coding is a simple lossless data compression technique that tries to take advantage of entropy by using a Variable-Length encoding to build a code table to encode a source file symbols. In this paper, we have re-visited Huffman coding and enhance it by considering the second order form of characters rather the first order form of characters...

This paper suggests four different methods to solve nonlinear integro-differential equations, namely, He's variational iteration method, Adomian decomposition method, He's homotopy perturbation method and differential transform method. To assess the accuracy of each method, a test example with known exact solution is used. The study outlines signif...

In this paper, we introduce a novel approach for combining web usage mining and content mining. The approach is based on generating recommendations that take into consideration users' navigation history as well as contents of pages visited. The integration of usage and content data can be performed at the offline phase or at the online phase of the...

In this paper we propose parallel algorithm for the solution of partial differential equations over a rectangular domain using the Crank–Nicholson method by cooperation with the DuFort–Frankel method and apply it on a model problem, namely, the heat conduction equation. One of the well known parallel techniques in solving partial differential equat...

In this paper, we present a parallel iterative solution for large banded systems of linear equations based on incomplete LU-factorization (ILU). A master—workers parallel computing scheme is used. The proposed algorithm incurs reduced storage and communication overhead as compared to previous methods. The reduction in communication overhead has bee...

In this paper, we present and evaluate a new parallel algorithm for Gauss–Huard method with scaled partial pivoting strategy for the solution of linear systems of equations. The algorithm is generic in the sense that matrix distribution methods are decoupled from the algorithm details which makes it applicable to a wide spectrum of distribution fun...

ABSTRACT: We propose Colored Petri Net (CPN) models for replicated and centralized database systems and conduct a comparative study of their performance. The designed CPN models capture the dynamics of the studied database systems and estimate their expected performance with an appropriate level of abstraction. A number of simulation experiments we...

In this paper, we develop and evaluate a parallel algorithm for GESPP on a cluster of Silicon Graphics workstations using PVM as a parallel programming environment. The proposed algorithm reduces the computation time to O(n³ / p) and the communication time to O(n) including scaling, searching for the pivot element, row interchanging, and...

We describe an improved algorithm for the direct solution of general sparse systems. The improved algorithm utilizes a reordering scheme to improve the performance of partial pivoting codes for the LU-factorization and to minimize the fill-in while preserving the matrix sparsity. The experimental results indicate that the new algorithm is faster th...

In this paper, some mathematical results concerning the quasi-stationary probabilities are reviewed and a central limit theorem is obtained for a sequence of random variables defined on a finite absorbing Markov chains. We consider absorbing chains with absorbing subchains when the absorbing subchain is not regard as a single absorbing state. The t...

The asymptotic normality of maximum likelihood estimators (MLE) for multiparameter Markov chains is proved. The proof is based on a sketch of C. R. Rao [Linear statistical inference and its applications. (1973; Zbl 0256.62002)]. Some details and gaps had to be filled out.

We describe an improved algorithm to accelerate the convergence of the iterative refinement method. The improved algorithm is simple, practical, numerically stable and speed up the convergence. Experimental results indicate that thenew algorithm is usually faster than the classical one.

In this paper we derive the reverse process of absorbing Markov chains with r, r>1 absorbing states and study such a process conditional on an eventual absorption into a specified state

In this paper we derive the limiting distributions for absorbing Markov chains with r absorbing states, where r>1 and study different types of the limiting distributions conditional on an eventual absorption into a specified state. For such a problem we consider the limiting ratio of means and the limiting conditional mean ratios.

We derive the quasi-stationary distribution of absorbing Markov chains with more than one absorbing state and study the different types of quasi-stationary distributions conditional on an eventual absorption into a specified state, using the method of limiting conditional probabilities. The problem of quasi-stationarity has been motivated by some b...

In this paper an empirical results concerning the maximum likelihood estimator (MLE) and the Jackknife estimators for the parameters of the first and second order autoregressive process are investigated. It is found that the Jackknife estimators all through have smaller bias where as the mean square error has increased.

This paper is an application of the McNemar test which is a variation of the Sign test for testing the existence of absorbing subchains in a given Markov chain associated with a subset of the State Space by using a sequence of observations coming from the given Markov chain under the condition that there are no ?ties? between the pairs of data.

In this paper an empirical comparison is done between maximum likelihood estimator (MLE) and the Bayes estimators for the parameters of the first order autoregressive process suggested by Abu-Salih and Abd-Alla in case of short series.

Taylor expansion method for solving second order linear partial differential equations under given conditions has been investigated by Kesan. In this paper we present Kesan's work, which gives the theoretical meaning of the Taylor expansion method. We provide a detailed analysis of Kesan's work, and we reconstruct Kesan's relations as theorems and...

In this paper, we present parallel implementation of the Gauss-Huard algorithm with scaled partial pivoting strategy on a cluster of Linux workstations using PVM as a parallel programming environment. We developed and verified a timing model to accurately estimate the execution time of the proposed algorithm. The obtained experimental results for t...