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