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

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.