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Dual solutions for nonlinear boundary value problems by the Adomian decomposition method

Abdul-Majid Wazwaz (Department of Mathematics, Saint Xavier University, Chicago, Illinois, USA)
Randolph Rach (The George Adomian Center for Applied Mathematics, Hartford, Michigan, USA)
Lazhar Bougoffa (Department of Mathematics, Al-Imam Mohammad Inb Saud Islamic University, Riyadh, Saudi Arabia)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 7 November 2016

Abstract

Purpose

The purpose of this paper is to use the Adomian decomposition method (ADM) for solving boundary value problems with dual solutions.

Design/methodology/approach

The ADM has been previously demonstrated to be eminently practical with widespread applicability to frontier problems arising in scientific applications. In this work, the authors seek to determine the relative merits of the ADM in the context of several important nonlinear boundary value models characterized by the existence of dual solutions.

Findings

The ADM is shown to readily solve specific nonlinear BVPs possessing more than one solution. The decomposition series solution of these models requires the calculation of the Adomian polynomials appropriate to the particular system nonlinearity. The authors show that the ADM solves these models for any analytic nonlinearity in a practical and straightforward manner. The conclusions are supported by several numerical examples arising in various scientific applications which admit dual solutions.

Originality/value

This paper presents an accurate work for solving nonlinear BVPs that possess dual solutions. The authors have demonstrated the widespread applicability of the ADM for solving various forms of these nonlinear equations.

Keywords

Citation

Wazwaz, A.-M., Rach, R. and Bougoffa, L. (2016), "Dual solutions for nonlinear boundary value problems by the Adomian decomposition method", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 26 No. 8, pp. 2393-2409. https://doi.org/10.1108/HFF-10-2015-0439

Publisher

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Emerald Group Publishing Limited

Copyright © 2016, Emerald Group Publishing Limited