El-Kalla, I.L. (2012) A New Approach for Solving a Class of Nonlinear Integro-Differential Equations. Communications in Nonlinear Science and Numerical Simulation, 17, 4634-4641.
https://doi.org/10.1016/j.cnsns.2012.05.016

has been cited by the following article:

• TITLE: Solution of a Nonlinear Delay Differential Equation Using Adomian Decomposition Method with Accelerated Formula of Adomian Polynomial

  AUTHORS: I. L. El-Kalla, Khaled M. Abd Elgaber, Ali R. Elmahdy, Ahmed Y. Sayed

  KEYWORDS: Adomian Polynomial, El-Kalla Polynomial, A Nonlinear Delay Differential Equation

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.9 No.4, November 26, 2019

  ABSTRACT: The aim of this paper is to apply Adomian decomposition method (ADM) for solving some classes of nonlinear delay differential equations (NDDEs) with accelerated Adomian polynomial called El-kalla polynomial proposed by El-kalla [1]. The main advantages of El-kalla polynomials can be summarized in the following main three points: 1) 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; 2) Solution using El-Kalla polynomials converges faster than the traditional Adomian polynomials; 3) 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 using the Adomian decomposition method using the two polynomials (Adomian polynomial and El-kalla polynomial). In all applied cases, we obtained an excellent performance that may lead to a promising approach for many applications.