热敏电阻问题的有限差分解法及其收敛性分析

FINITE DIFFERENCE METHOD AND ITS CONVERGENT ERROR ANALYSES FOR THERMISTOR PROBLEM

The thermistor problem is an initial-boundary value problem of coupled nonlinear differential equations.The nonlinear PDEs consist of a heat equation with the Joule heating as a source and a current conservation equation with temperature-dependent electrical conductivity.This problem has important applications in industry.In this paper,A new finite difference scheme is proposed on nonuniform rectangular partition for the thermistor problem.In the theoretical analyses,the second-order error estimates are obtained for electrical potential in discrete L2 and H1 norms,and for the temperature in L2 norm.In order to get these second-order error estimates,the Joule heating source is used in a changed equivalent form.