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A New Optimal Scheme for Solving Nonlinear Heat Conduction Problems

Chih-Wen Chang1,2, Chein-Shan Liu3

Computing Technology Integration Division, National Center for High-Performance Computing, Taichung 40763, Taiwan
Corresponding author, Tel.:+886-4-24620202#860. E-mail address:
Department of Civil Engineering, National Taiwan University, Taipei 10617, Taiwan

Computer Modeling in Engineering & Sciences 2012, 88(4), 269-292.


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.


Cite This Article

Chang, C., Liu, C. (2012). A New Optimal Scheme for Solving Nonlinear Heat Conduction Problems. CMES-Computer Modeling in Engineering & Sciences, 88(4), 269–292.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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