# Belal Mohammed BatihaJadara University · Department of Mathematics

Belal Mohammed Batiha

Doctor of Mathematics

## About

38

Publications

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832

Citations

Citations since 2016

Introduction

Additional affiliations

September 2018 - present

March 2011 - March 2017

## Publications

Publications (38)

The generalized exponential function in a complex domain is called the Mittag-Leffler function (MLF). The implementations of MLF are significant in diverse areas of science. Over the past few decades, MLF and its analysis with generalizations have become an increasingly rich research area in mathematics and its allied fields. In the geometric theor...

The solution of quadratic Riccati differential equations can be found by classical numerical methods like Runge-Kutta method and the forward Euler method. Batiha et al. [7] applied variational iteration method (VIM) for the solution of General Riccati Equation. In the paper of El-Tawil et al. [19] they used the Adomian decomposition method (ADM) to...

In this article, the Daftardar-Gejji and Jafari method (DJM) is used to obtain an approximate analytical solution of the sine-Gordon equation. Some examples are solved to demonstrate the accuracy of DJM. A comparison study between DJM, the variational iteration method (VIM), and the exact solution are presented. The comparison of the present symmet...

This paper deals with two-step hybrid block method with one generalized off-step points for solving second order initial value problem. In derivation of this method, power series of order nine are interpolated at the first two step points while its second and third derivatives are collocated at all point in the selected interval. The new developed...

In this paper, the nonlinear Bratu type equation is numerically solved via quintic B-spline method. It is shown that the proposed technique has fourth order convergence. The efficiency and applicability of this method is confirmed by considering some examples. The proposed procedure provides better results in comparison to some existing methods.

The Hadamard product is employed in this study to describe a new class of analytic functions that include linear operator. Some of the properties related to this new class are also investigated. In the second result of this paper, applications on hypergeometric functions that employ the popular hypergeometric functions with the operator are include...

In this article, we present the solution of nonlinear oscillators by new numerical method called the Daftardar-Gejji and Jafari method (DJM). The results derived by DJM are compared with variational iteration method (VIM), Homotopy perturbation method (HPM) and Runge-Kutta method in order to prove the accuracy of DJM.

In this paper, fractional complex transform (FCT) with help of variational iteration method (VIM) is used to obtain numerical and analytical solutions for the fractional Zakharov-Kuznetsov equations. Fractional complex transform (FCT) is proposed to convert fractional Zakharov-Kuznetsov equations to its differential partner and then applied VIM to...

A new efficient method called the multistage variational iteration method (MVIM) is applied to the solution of quadratic Riccati differential equations. A comparison between MVIM solution with classical variational iteration method (VIM) and exact solution has been made and show that the MVIM is a powerful method to the solution of nonlinear differ...

Magnetohydrodynamic (MHD) thin film flow of an electrically conducting Jeffrey fluid over a vertically moving belt is investigated when a slippage between the surface and the fluid occurs. Exact expression for velocity profile is obtained and is displayed graphically to illustrate the effects of interesting flow parameters. Expressions for some imp...

This paper provides an investigation regarding the modeling and analysis of a thin film flow of an Oldroyd 8-constant fluid on a vertically moving belt. The governing nonlinear problem is solved by using Variational Iteration Method (VIM). The results of the present method are then compared with those obtained by Adomian Decomposition Method (ADM)...

In this paper, fractional complex transform (FCT) with help of varia-tional iteration method (VIM) is used to obtain numerical and analytical solutions for the fractional Zakharov–Kuznetsov equations. Fractional complex transform (FCT) is proposed to convert fractional Zakharov– Kuznetsov equations to its differential partner and then applied VIM t...

In this paper the problem of prey and predator is presented and the differential transformation method (DTM) is employed to solve the sys-tem of nonlinear ordinary differential equations governing the problem. Numerical comparisons with Adomian decomposition method (ADM) and power series mthod are presented. Some plots are presented to show the pop...

In this paper, the multistage variational iteration method (MVIM) is applied to the solution of quadratic Riccati differential equations. The solution of quadratic Riccati differential equation obtained using the classical variational iteration method (VIM) give good approximations only in the neighborhood of the initial position. The solution obta...

The variational iteration method (VIM) is applied to solve nonlinear oscillators. Only one iteration leads to high accuracy of the solutions. The accuracy of the obtained solutions is demonstrated by several examples.

In this paper, we present a comparative study between the differential transformation method (DTM), the variational iteration method and Adomian decomposition method (ADM). The study outlines the significant features of the three methods. The analysis will be illustrated by investigating the one species Lotka-Volterra equation. The numerical result...

In this paper the problem of the spread of a non-fatal disease in a population which is assumed to have constant size over the period of the epidemic is considered. The differential transformation method (DTM) is used to compute an approximation to the solution of the system of nonlinear ordinary differential equations governing the problem. The re...

In this paper, exact analytical solutions of Cauchy-Euler differential equation are obtained by the differential transformation method (DTM). The method is capable of reducing the size of calculations and handles linear or nonlinear, homogeneous or nonhomogeneous equations, in a direct manner. Four examples are presented to illustrate the efficienc...

In this paper, we present a numeric-analytic solution of the well-known Michaelis–Menten nonlinear biochemical reaction system based on differential transformation method (DTM). We shall compare the DTM against the homotopy-perturbation method (HPM). The numeri-cal results obtained from the DTM and HPM are in complete agreement.

In this paper, a Differential Transformation Method (DTM) is used to find the numerical solution of the linear ordinary differential equations, homogeneous or inhomogeneous.The method is capable of reducing the size of calculations and handles linear equations, homogeneous or inhomogeneous, in a direct manner. Five examples are considered for the n...

In this paper, the variational iteration method (VIM) is applied to obtain approximate analytical solution of Bratu-type equations without any discretization. Comparisons with the exact solutions reveal that VIM is very effective and convenient.

In this paper, variational iteration method (VIM) is applied to ob-tain approximate analytical solution of the (2 + 1)-dimensional poten-tial Kadomtsev-Petviashvili equation (PKP) without any discretization. Comparisons with the exact solutions reveal that VIM is very effective and convenient.

In this paper, variational iteration method (VIM) is presented as an alternative method for solving the nonlinear Klein-Gordon equation. The method is demonstrated by several examples. A new technique for choosing the initial approximation of VIM is presented. Comparisons with the exact solutions reveal that VIM is very effective and convenient.

The variational iteration method (VIM) is applied to the numerical simulation of linear third-order dispersive partial differential equations (PDEs). The VIM produces an approximate solution of the equation without any discretization. The VIM is based on the incorporation of a general Lagrange multiplier in the construction of correction functional...

In this paper, solutions of a class of singular initial value problems (IVPs) in the second-order ordinary differential equations (ODEs) by variational it-eration method (VIM) is presented. Comparisons with exact solution show that the VIM is a powerful method for the solution of linear and nonlinear equations.

In this paper, He’s variational iteration method (VIM) is applied to the generalized Burgers–Huxley equation. The VIM produces an approximate solution of the equation without any discretization. The VIM is based on the incorporation of a general Lagrange multiplier in the construction of correction functional for the equation. Comparisons with the...

In this Letter, a general framework of the variational iteration method (VIM) is presented for solving systems of linear and nonlinear partial differential equations (PDEs). In VIM, a correction functional is constructed by a general Lagrange's multiplier which can be identified via a variational theory. VIM yields an approximate solution in the fo...

This paper compares the variational iteration method (VIM) with the Adomian decomposition method (ADM) for solving nonlinear integro- dierential equations. From the computa- tional viewpoint, the VIM is more ecient, convenient and easy to use.

This paper applies the variational iteration method to multispecies Lotka–Volterra equations. Comparisons with the Adomian decomposition and the fourth-order Runge–Kutta methods show that the variational iteration method is a powerful method for nonlinear equations.

In this Letter, variational iteration method (VIM) is applied to obtain approximate analytical solution of the sine-Gordon equation without any discretization. Comparisons with the exact solutions reveal that VIM is very effective and convenient.

In this paper, the variational iteration method (VIM) is applied to obtain the approximate analytical solution of the coupled sine-Gordon equation without any discretization. VIM is based on the incorporation of a general Lagrange multiplier in the construction of the correction functional for the equation. Comparisons with the Adomian decompositio...

This paper implements the multistage variational iteration method (MVIM) to solve a class of nonlinear system of first-order ordinary differential equations (ODEs). The domain of validity of the solutions via the standard variational iteration method (VIM) is extended by the simple multistage strategy. Comparisons with the exact solution and the fo...

In this Letter, variational iteration method (VIM) is employed to obtain analytical solution for the heat- and wave-like equations with singular behaviors. Comparisons with the exact solution show that the VIM is a powerful method for the solution of linear and nonlinear singular equations.

In this work we solve a fourth-order parabolic partial differential equation using Adomian decomposition method (ADM). The ADM yields an explicit solution in the form of series which converges rapidly. Based on our numerical results, the ADM outperforms the Alternating Group Explicit (AGE) method. We also show that the modified ADM can give the exa...

By means of variational iteration method the solution of generalized Huxley equation are obtained, comparison with the Adomian decomposition method is made, showing that the former is more effective than the later. In this paper, He’s variational iteration method is introduced to overcome the difficulty arising in calculating Adomian polynomials.

The variational iteration method (VIM) is applied to the solution of general Riccati differential equations. The equations under consideration includes one with variable coefficient and one in matrix form. In VIM, a correction functional is constructed by a general Lagrange multiplier which can be identified via a variational theory. The VIM yields...

In a recent paper, Ismail et al. [Adomian decomposition method for Burgers-Huxley and Burgers-Fisher equations, Appl. Math. Comput. 159 (2004) 291-301] employed the Adomian decomposition method (ADM) to solve, in particular, a generalized nonlinear Huxley equation. The purpose of this note is to correct Ismail et al.'s numerical solutions of the ge...

## Projects

Projects (2)