Jun-Sheng Duan1,2, Randolph Rach3, Abdul-Majid Wazwaz4
CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.1, pp. 77-118, 2013, DOI:10.3970/cmes.2013.094.077
Abstract In this paper, we propose a new modification of the Adomian decomposition method for solution of higher-order nonlinear initial value problems with variable system coefficients and solutions of systems of coupled nonlinear initial value problems. We consider various algorithms for the Adomian decomposition series and the series of Adomian polynomials to calculate the solutions of canonical first- and second-order nonlinear initial value problems in order to derive a systematic algorithm for the general case of higher-order nonlinear initial value problems and systems of coupled higher-order nonlinear initial value problems. Our new modified recursion scheme is designed to decelerate the Adomian… More >
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