Numerical Treatment of Initial Value Problems of Nonlinear Ordinary Differential Equations by Duan-Rach-Wazwaz Modified Adomian Decomposition Method — Oak Academic Publishing
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Numerical Treatment of Initial Value Problems of Nonlinear Ordinary Differential Equations by Duan-Rach-Wazwaz Modified Adomian Decomposition Method
Department of Mathematics, Faculty of Arts and Sciences, Bolu Abant İzzet Baysal University, Bolu, Turkey
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Department of Mathematics, Faculty of Arts and Sciences, Bolu Abant İzzet Baysal University, Bolu, Turkey
1 Department of Mathematics, Faculty of Arts and Sciences, Bolu Abant İzzet Baysal University, Bolu, Turkey
2 Department of Mathematics, Faculty of Arts and Sciences, Bolu Abant İzzet Baysal University, Bolu, Turkey
We employ the Duan-Rach-Wazwaz modified Adomian decomposition method for solving initial value problems for the systems of nonlinear ordinary differential equations numerically. In order to confirm practicality, robustness and reliability of the method, we compare the results from the modified Adomian decomposition method with those from the MATHEMATICA solutions and also from the fourth-order Runge Kutta method solutions in some cases. Furthermore, we apply Padé approximants technique to improve the solutions of the modified decomposition method whenever the exact solutions exist.
KeywordsAdomian Decomposition MethodDuan-Rach-Wazwaz Modified Adomian Decomposition MethodInitial Value ProblemNonlinear Ordinary Differential EquationMathematica Solution4-th Order Runge Kutta MethodPadéApproximants
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