Green’s Function Iterative Method for Solving a Class of Boundary Value Problems Arising in Heat Transfer

Authors

Marwan Abukhaled, Department of Mathematics and Statistics, American University of Sharjah, Sharjah, United Arab EmiratesFollow

Author Country (or Countries)

United Arab Emirates

Abstract

In this study, a new algorithm based on Green’s function fixed point iterations is developed and implemented to solve a class of nonlinear boundary value problems that arise in heat transfer. The method will be employed to determine the efficiency of convective straight fins with temperature dependent thermal conductivity. The main idea of this method is to find an appropriate Green’s function that will be incorporated into a linear integral operator. By applying the fixed point theorem, an iterative formula for successive approximations will be obtained. Effectiveness and accuracy were noted when approximate results obtained by the proposed method reveal significant agreement with existed exact solutions and/or approximate solutions obtained by other renowned methods.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/110128

Recommended Citation

Abukhaled, Marwan (2017) "Green’s Function Iterative Method for Solving a Class of Boundary Value Problems Arising in Heat Transfer," Applied Mathematics & Information Sciences: Vol. 11: Iss. 1, Article 28.
DOI: http://dx.doi.org/10.18576/amis/110128
Available at: https://digitalcommons.aaru.edu.jo/amis/vol11/iss1/28