Solving Nonlinear Differential Equations Using Adomian Decomposition Method Through Sagemath
M.Kaliyappan1, S. Hariharan2
1M.Kaliyappan, Department of Mathematics, Vellore Institute of Technology, Chennai (Tamil Nadu), India.
2S.Hariharan, Department of Mathematics, Amrita Vishwa Vidyapeetham, Coimbatore (Tamil Nadu), India.
Manuscript received on 07 April 2019 | Revised Manuscript received on 20 April 2019 | Manuscript published on 30 April 2019 | PP: 510-515 | Volume-8 Issue-6, April 2019 | Retrieval Number: E3192038519/19©BEIESP
Open Access | Ethics and Policies | Cite | Mendeley | Indexing and Abstracting
© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: The Adomian decomposition method (ADM) proposed by George Adomian is one of the teachnique to solve linear as well as nonlinear differential equations that are encountered in the field of Physics, Biology and Engineering etc. Computation of Adomian Polynomials for each of the nonlinear terms is a vital activity when solving nonlinear problems using ADM method. In this paper the authors presents a SageMath program for computing Adomian polynomials through integer partition method for single variable case. The SageMath code developed in this paper is felt to be an efficient symbolic computation for generating Adomian polynomials. Also, SageMath package for solving nonlinear differential equations through Adomian decomposition method are presented in this paper. Examples of solving nonlinear ordinary, partial and fractional differential equations are given and the results confirm the applicability of the developed program.
Keyword: Adomian Decomposition Method (ADM), SageMath, Nonlinear Terms, Adomian Polynomials, Differential Equations.
Scope of the Article: Cryptography and Applied Mathematics