A method for solving nonlinear integro‐differential equations

Abstract

Purpose -The purpose of this paper is to present a method for solving nonlinear integro-differential equations with constant/variable coefficients and with initial/boundary conditions. Design/methodology/approach -The method converts the given problem into a system of nonlinear algebraic equations. By solving this system, the solution is determined. Comparing the methodology with some known techniques shows that the present approach is simple, easy to use and highly accurate. Findings -The proposed technique allows an approximate solution in a series form to be obtained. Test problems are solved to illustrate the pertinent features of the method. The accuracy of the numerical results indicates that the technique is efficient and well suited for solving nonlinear integro-differential equations. Originality/value -The present approach provides a reliable technique which avoids the tedious work needed by the classical techniques.

A Comparison between Adomian Decomposition and Tau Methods

“…Borhanifar and Abazari [25] implemented the differential transform method for solving nonlinear integro-differential equations with the kernel functions including derivative type of unknown solution. Ben Zitoun and Cherruault [26] presented a method for solving nonlinear integro-differential equations with constant or variable coefficients with initial or boundary conditions. El-Kalla [27] introduced a new technique for solving a class of quadratic integral and integrodifferential equations.…”