A New Optimal Scheme for Solving Nonlinear Heat Conduction Problems

作者：Chang Chih Wen^*; Liu Chein Shan

来源：Computer Modeling in Engineering & Sciences, 2012, 88(4): 269-291.

• Nonlinear algebraic equations
• Nonlinear heat conduction equation
• Iterative algorithm
• Optimal vector driven algorithm (OVDA)
• Invariant manifold

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 gamma and alpha. Several numerical instances of nonlinear systems under noise are examined, finding that the OVDA has a fast convergence rate, great computation accuracy and efficiency.

• 出版日期2012-11