Solution of a class of nonlinear differential equations using an accelerated version of Adomian decomposition method
R. Elmahdy, A., Y. Sayed, A., M. AbdElgaber, K., L. El-Kalla, I. (2020). Solution of a class of nonlinear differential equations using an accelerated version of Adomian decomposition method. EKB Journal Management System, 167(0), 15-33. doi: 10.21608/erj.2020.139528
A. R. Elmahdy; A. Y. Sayed; K. M. AbdElgaber; I. L. El-Kalla. "Solution of a class of nonlinear differential equations using an accelerated version of Adomian decomposition method". EKB Journal Management System, 167, 0, 2020, 15-33. doi: 10.21608/erj.2020.139528
R. Elmahdy, A., Y. Sayed, A., M. AbdElgaber, K., L. El-Kalla, I. (2020). 'Solution of a class of nonlinear differential equations using an accelerated version of Adomian decomposition method', EKB Journal Management System, 167(0), pp. 15-33. doi: 10.21608/erj.2020.139528
R. Elmahdy, A., Y. Sayed, A., M. AbdElgaber, K., L. El-Kalla, I. Solution of a class of nonlinear differential equations using an accelerated version of Adomian decomposition method. EKB Journal Management System, 2020; 167(0): 15-33. doi: 10.21608/erj.2020.139528

Solution of a class of nonlinear differential equations using an accelerated version of Adomian decomposition method

Engineering Research Journal
Article 2, Volume 167, Issue 0, September 2020, Page 15-33  XML PDF (463.66 K)
Document Type: Original Article
DOI: 10.21608/erj.2020.139528
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Authors
A. R. Elmahdy* 1; A. Y. Sayed2; K. M. AbdElgaber2; I. L. El-Kalla3
1Department of Engineering Mathematics and Physics, Faculty of Engineering El-Mataria, PO 11718 Cairo, Helwan University, Egyp
2Department of Engineering Mathematics and Physics, Faculty of Engineering El-Mataria, PO 11718 Cairo, Helwan University, Egypt
3Department of Physics & Engineering Mathematics, Faculty of Engineering, Mansoura University, PO 35516, Mansoura, Egyp
Abstract
In this work, we proposed a reliable polynomials called El-kalla polynomials which are faster than the traditional Adomian polynomials in solving some classes of nonlinear differential equations by Adomian decomposition method (ADM). The main advantages of El-kalla polynomials can be summerized in the following main three points:  El-kalla polynomials are recursive and do not have derivative terms so, El-kalla formula is easy in programming and save much time on the same processor compared with the traditional Adomian polynomials formula.  Solution using El-Kalla polynomials converges faster than the traditional Adomian polynomials.  El-Kalla polynomials used directly in estimating the maximum absolute truncated error of the series solution. Some convergence remarks are studied and some numerical examples are solved to verify the above advantages. In all applied cases, we obtained an excellent performance that may lead to a promising approach for many applications.
Keywords
Adomian polynomial; El-Kalla polynomial; nonlinear differential equations
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