TY - EJOU AU - Chang, Chih-Wen AU - Liu, Chein-Shan TI - A New Optimal Scheme for Solving Nonlinear Heat Conduction Problems T2 - Computer Modeling in Engineering \& Sciences PY - 2012 VL - 88 IS - 4 SN - 1526-1506 AB - 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. KW - Nonlinear algebraic equations KW - Nonlinear heat conduction equation KW - Iterative algorithm KW - Optimal vector driven algorithm (OVDA) KW - Invariant manifold DO - 10.3970/cmes.2012.088.269