A general numerical algorithm for nonlinear differential equations by the variational iteration method

Abstract

Purpose

The purpose of this paper is to suggest a general numerical algorithm for nonlinear problems by the variational iteration method (VIM).

Design/methodology/approach

Firstly, the Laplace transform technique is used to reconstruct the variational iteration algorithm-II. Secondly, its convergence is strictly proved. Thirdly, the numerical steps for the algorithm is given. Finally, some examples are given to show the solution process and the effectiveness of the method.

Findings

No variational theory is needed to construct the numerical algorithm, and the incorporation of the Laplace method into the VIM makes the solution process much simpler.

Originality/value

A universal iteration formulation is suggested for nonlinear problems. The VIM cleans up the numerical road to differential equations.

Citation

He, J.-H. and Latifizadeh, H. (2020), "A general numerical algorithm for nonlinear differential equations by the variational iteration method", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 30 No. 11, pp. 4797-4810. https://doi.org/10.1108/HFF-01-2020-0029