Dual solutions for nonlinear boundary value problems by the Adomian decomposition method. Issue 8 (7th November 2016)

• Record Type: Journal Article
• Authors: Wazwaz, Abdul-Majid; Rach, Randolph; Bougoffa, Lazhar
• Is Part Of: International journal of numerical methods for heat & fluid flow. Volume 26:Issue 8(2016)
• Page Start: 2393
• Page End: 2409
• Publication Date: 2016-11-07
• Subjects: Adomian decomposition method -- Heat transfer -- Adomian polynomials -- Diffusion and reaction -- Mixed convection flows; Heat -- Transmission -- Mathematics -- Periodicals; Fluid dynamics -- Mathematics -- Periodicals; 536.2
• DOI: 10.1108/HFF-10-2015-0439
• Languages: English
• ISSNs: 0961-5539

Abstract

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.