A new recursive scheme for solving the general fractional differential equation of the nonlinear Lienard’s equation

Abstract

Purpose

The purpose of this paper is to solve an initial-value problem for the general fractional differential equation of the nonlinear Lienard's equation.

Design/methodology/approach

A new recursive scheme is presented by combining the Adomian decomposition method with a magnificent recurrence formula and via the solutions of the well-known generalized Abel equation.

Findings

It is shown that the proposed method may offer advantages in computing the components yn; n = 1; 2; … in an easily computed formula. Also, the numerical experiments show that with few iterations of the recursive method, this technique converges swiftly and accurately.

Originality/value

The approach is original, and a reasonably accurate solution can be achieved with only two components. Moreover, the proposed method can be applied to several nonlinear models in science and engineering.

Citation

Mennouni, A. and Bougoffa, L. (2022), "A new recursive scheme for solving the general fractional differential equation of the nonlinear Lienard’s equation", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 32 No. 11, pp. 3470-3483. https://doi.org/10.1108/HFF-02-2022-0076