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Adomian Decomposition Method with Green’s Function for Solving Tenth-Order Boundary Value Problems

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Applied Mathematics 2014年第10期5卷 1437-1447页

作者： waleed al-hayani Department of Mathematics College of Computer Science and Mathematics University of Mosul Mosul Iraq

In this paper, the Adomian decomposition method with Green’s function (Standard Adomian and Modified Technique) is applied to solve linear and nonlinear tenth-order boundary value problems with boundary conditions defined at any order derivatives. The numerical results obtained with a small amount of computation are compared with the exact solutions to show the efficiency of the method. The results show that the decomposition method is of high accuracy, more convenient and efficient for solving high-order boundary value problems.

关键词： Adomian Decomposition Method Adomian’s Polynomials Tenth-Order Boundary Value Problems Green’s Function

Solving <i>nth</i>-Order Integro-Differential Equations Using the Combined Laplace Transform-Adomian Decomposition Method

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Applied Mathematics 2013年第6期4卷 882-886页

作者： waleed al-hayani Department of Mathematics College of Computer Science and Mathematics University of Mosul Mosul Iraq

In this paper, the Combined Laplace Transform-Adomian Decomposition Method is used to solve nth-order integro-differential equations. The results show that the method is very simple and effective.

关键词： Integro-Differential Equations Laplace Transform Method Adomian Decomposition Method

Homotopy Analysis Method for Solving Initial Value Problems of Second Order with Discontinuities

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Applied Mathematics 2019年第6期10卷 419-434页

作者： waleed al-hayani Rasha Fahad Department of Mathematics College of Computer Science and Mathematics Mosul University Mosul Iraq

In this paper, the standard homotopy analysis method was applied to initial value problems of the second order with some types of discontinuities, for both linear and nonlinear cases. To show the high accuracy of the solution results compared with the exact solution, a comparison of the numerical results was made applying the standard homotopy analysis method with the iteration of the integral equation and the numerical solution with the Simpson rule. also, the maximum absolute error, , the maximum relative error, the maximum residual error and the estimated order of convergence were given. The research is meaningful and I recommend it to be published in the journal.

关键词： Homotopy Analysis Method Initial Value Problems Heaviside Step Function Dirac Delta Function Simpson Rule

Analytical Solution for the Time-Dependent Emden-Fowler Type of Equations by Homotopy Analysis Method with Genetic algorithm

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Applied Mathematics 2017年第5期8卷 693-711页

作者： waleed al-hayani Laheeb alzubaidy Ahmed Entesar Department of Mathematics College of Computer Science and Mathematics University of Mosul Mosul Iraq Department of Software Engineering College of Computer Science and Mathematics University of Mosul Mosul Iraq

In this paper, Homotopy Analysis method with Genetic algorithm is presented and used to obtain an analytical solution for the time-dependent Emden-Fowler type of equations and wave-type equation with singular behavior at x = 0. The advantage of this single global method employed to present a reliable framework is utilized to overcome the singularity behavior at the point x = 0 for both models. The method is demonstrated for a variety of problems in one and higher dimensional spaces where approximate-exact solutions are obtained. The results obtained in all cases show the reliability and the efficiency of this method.

关键词： Homotopy Analysis Method Genetic algorithm Emden-Fowler Equation Wave-Type Equation Adomian Polynomials Noise Terms Padé Approximants Simpson Rule