Title: Analytical solutions to nonlinear problems by the generalised form of HAM: a note

Authors: Anant Kant Shukla; T.R. Ramamohan; S. Srinivas

Addresses: Department of Mathematics, School of Advanced Sciences, VIT Bhopal University, Kothrikalan, Sehore – 466 114, Madhya Pradesh, India ' Chemical Engineering Department, MSRIT, MSR Nagar, Bangalore – 560054, Karnataka, India ' VIT-AP University, Inavolu Village, Near AP Govt. Secretariat, Amaravati – 522 237, Andhra Pradesh, India

Abstract: The objective of this article is to obtain analytical solutions for a set of nonlinear problems by using 'further generalisation of HAM'. In comparison to the Homotopy analysis method (HAM) solutions, more accurate solutions are obtained by introducing an extra term in the frame of HAM. We consider a set of three nonlinear problems of which first two are governed by single nonlinear ordinary differential equation (they are two cases of the forced Van der Pol Duffing oscillator) and third one is governed by a system of four coupled nonlinear ordinary differential equations. A maximum reduction of approximately 25% in the square residual error is obtained by using the generalised form of HAM compared to the square residual error without the generalised form.

Keywords: further generalisation of HAM; homotopy analysis method; square residual error.

DOI: 10.1504/IJCSM.2019.098741

International Journal of Computing Science and Mathematics, 2019 Vol.10 No.2, pp.160 - 173

Received: 11 Jan 2017
Accepted: 19 Jul 2017
Published online: 02 Apr 2019 *

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