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Rational Approximations for Heat Radiation and Troesch’s Equations

Electronic Instrumentation and Atmospheric Sciences School, Universidad Veracruzana, Cto. Gonzalo Aguirre Beltrán S/N, 91000 Xalapa, Veracruz, México

E-mail Address: hvazquez@uv.mx

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Hüseyin Koçak

Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK

Departamento de Matemática Aplicada, Facultad de Matemáticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, Madrid 28040, Spain

E-mail Address: H.Kocak@bath.ac.uk

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, and

Inan Ates

Mathematical Institute, Utrecht University, Budapestlaan 6, 3584 CD, Utrecht, The Netherlands

E-mail Address: I.Ates@uu.nl

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https://doi.org/10.1142/S0219876216500390Cited by:1 (Source: Crossref)

Abstract

In this paper, a new tool for the solution of nonlinear differential equations is presented. It is named rational homotopy perturbation method (RHPM). It delivers a high precision representation of the nonlinear differential equation using a few linear algebraic terms. In order to assess the benefits of this proposal, three nonlinear problems are solved and compared against other semi-analytic methods or numerical methods. Furthermore, in order to deal with BVP problems, we propose a modification of RHPM method. The obtained results show that RHPM is a powerful tool capable to generate highly accurate rational solutions.

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