Open Access

ARTICLE

A New Optimal Scheme for Solving Nonlinear Heat Conduction Problems

Chih-Wen Chang^1,2, Chein-Shan Liu³

1 Computing Technology Integration Division, National Center for High-Performance Computing, Taichung 40763, Taiwan
2 Corresponding author, Tel.:+886-4-24620202#860. E-mail address: 0903040@nchc.narl.org.tw
3 Department of Civil Engineering, National Taiwan University, Taipei 10617, Taiwan

Computer Modeling in Engineering & Sciences 2012, 88(4), 269-292. https://doi.org/10.3970/cmes.2012.088.269

Abstract

In this article, we utilize an optimal vector driven algorithm (OVDA) to cope with the nonlinear heat conduction problems (HCPs). From this set of nonlinear ordinary differential equations, we propose a purely iterative scheme and the spatial-discretization of finite difference method for revealing the solution vector x, without having to invert the Jacobian matrix D. Furthermore, we introduce three new ideas of bifurcation, attracting set and optimal combination, which are restrained by two parameters g and a. Several numerical instances of nonlinear systems under noise are examined, finding that the OVDA has a fast convergence rate, great computation accuracy and efficiency.

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Keywords

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