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Babolian, E. and Biazar, J. (2002) Solving the Problem of Biological Species Living together by Adomian Decomposition Method. Applied Mathematics and Computation, 343, 129-339. https://doi.org/10.1016/S0096-3003(01)00043-1

has been cited by the following article:

• TITLE: Numerical Treatment of Initial Value Problems of Nonlinear Ordinary Differential Equations by Duan-Rach-Wazwaz Modified Adomian Decomposition Method

  AUTHORS: Ömür Umut, Serpil Yaşar

  KEYWORDS: Adomian Decomposition Method, Duan-Rach-Wazwaz Modified Adomian Decomposition Method, Initial Value Problem, Nonlinear Ordinary Differential Equation, Mathematica Solution, 4-th Order Runge Kutta Method, Padé Approximants

  JOURNAL NAME: International Journal of Modern Nonlinear Theory and Application, Vol.8 No.1, February 1, 2019

  ABSTRACT: 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.