160 Int. J. Computing Science and Mathematics, Vol. 10, No. 2, 2019
Copyright © 2019 Inderscience Enterprises Ltd.
Analytical solutions to nonlinear problems by the
generalised form of HAM: a note
Anant Kant Shukla*
Department of Mathematics,
School of Advanced Sciences,
VIT Bhopal University,
Kothrikalan, Sehore – 466 114,
Madhya Pradesh, India
Email: kant85.shukla@gmail.com
*Corresponding author
T.R. Ramamohan
Chemical Engineering Department, MSRIT,
MSR Nagar,
Bangalore – 560054, Karnataka, India
Email: trr432@yahoo.com
S. Srinivas
VIT-AP University,
Inavolu Village, Near AP Govt. Secretariat,
Amaravati – 522 237, Andhra Pradesh, India
Email: srinusuripeddi@hotmail.com
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.
Reference to this paper should be made as follows: Shukla, A.K.,
Ramamohan, T.R. and Srinivas, S. (2019) ‘Analytical solutions to nonlinear
problems by the generalised form of HAM: a note’, Int. J. Computing Science
and Mathematics, Vol. 10, No. 2, pp.160–173.