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Numerical Solutions for Quadratic Integro-Differential Equations of Fractional Orders

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Open Journal of Applied Sciences 2017年第4期7卷 157-170页

作者： fatheah alhendi Wafa Shammakh Hind Al-Badrani Department of Mathematics King Abdulaziz University Jeddah Saudi Arabia Taibah University Madinah Saudi Arabia

In this article, variational iteration method (VIM) and homotopy perturbation method (HPM) solve the nonlinear initial value problems of first-order fractional quadratic integro-differential equations (FQIDEs). We use the Caputo sense in this article to describe the fractional derivatives. The solutions of the problems are derived by infinite convergent series, and the results show that both methods are most convenient and effective.

关键词： Fractional Quadratic Integro-Differential Equations Variational Iteration Method Homotopy Perturbation Method

Application of OHAM-DJ to the System of Burgers’ Equations

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American Journal of Computational Mathematics 2016年第3期6卷 212-223页

作者： fatheah Ahmad alhendi Bothayna Saleh Kashkari Aisha Abdullah Alderremy Department of Mathematics King Abdulaziz University Jeddah Saudi Arabia Department of Mathematics King Khalid University Abha Saudi Arabia

In this paper, the system of Burgers’ equations is solved by the optimal homotopy asymptotic method with Daftardar-Jafari polynomials OHAM-DJ. Two numerical examples are illustrated the efficient of this methods for ... 详细信息

关键词： Burgers’ Equations The Optimal Homotopy Asymptotic Method Daftardar-Jafari Polynomials

Numerical Treatment of Nonlinear Volterra-Fredholm Integral Equation with a Generalized Singular Kernel

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American Journal of Computational Mathematics 2016年第3期6卷 245-250页

作者： fatheah Ahmed Hendi Manal Mohamed Al-Qarni Department of Mathematics Faculty of Science King Abdul Aziz University Jeddah KSA Department of Mathematics Faculty of Science King Khaled University Abha KSA

In the paper, the approximate solution for the two-dimensional linear and nonlinear Volterra-Fredholm integral equation (V-FIE) with singular kernel by utilizing the combined Laplace-Adomian decomposition method (LADM) was studied. This technique is a convergent series from easily computable components. Four examples are exhibited, when the kernel takes Carleman and logarithmic forms. Numerical results uncover that the method is efficient and high accurate.

关键词： Singular Integral Equation Linear and Nonlinear V-FIE Adomian Decomposition Method (ADM) Carleman Kernel Logarithmic Kernel

Comparison between Adomian’s Decomposition Method and Toeplitz Matrix Method for Solving Linear Mixed Integral Equation with Hilbert Kernel

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American Journal of Computational Mathematics 2016年第2期6卷 177-183页

作者： fatheah Ahmed Hendi Manal Mohamed Al-Qarni Department of Mathematics Faculty of Science King Abdul Aziz University Jeddah Saudi Arabia Department of Mathematics Faculty of Science King Khaled University Abha Saudi Arabia

This paper proposes the combined Laplace-Adomian decomposition method (LADM) for solution two dimensional linear mixed integral equations of type Volterra-Fredholm with Hilbert kernel. Comparison of the obtained results with those obtained by the Toeplitz matrix method (TMM) demonstrates that the proposed technique is powerful and simple.

关键词： Singular Integral Equation Linear Volterra-Fredholm Integral Equation Adomian Decomposition Method Hilbert Kernel

Numerical Solution of Nonlinear Mixed Integral Equation with a Generalized Cauchy Kernel

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Applied Mathematics 2017年第2期8卷 209-214页

In this article, we present approximate solution of the two-dimensional singular nonlinear mixed Volterra-Fredholm integral equations (V-FIE), which is deduced by using new strategy (combined Laplace homotopy perturbation method (LHPM)). Here we consider the V-FIE with Cauchy kernel. Solved examples illustrate that the proposed strategy is powerful, effective and very simple.

关键词： Singular Integral Equation Linear and Nonlinear V-FIE Homotopy Perturbation Method (HPM) Cauchy Kernel