Numerical solution of the thermistor problem

摘要

In this paper, we consider the numerical solution of a one-dimensional thermistor (thermo-electric) problem with a bulk electrical conductivity, which is an inherently non-linear function of the temperature. The aims of this paper are to present approximate steady-state solutions to the thermistor problem using second order central difference weighted approximation methods (SOCDWAMs) and constrained integral methods (CIMs), and make their comparison with the exact solution. So, first of all we apply the CIM to each of the cold, warm, and hot phases to obtain approximate temperature distributions. And then, the CIM is constructed by assuming a quadratic polynomial approximation for the temperature profile. A variety of SOCDWAMs are applied to solve the problem using a bulk electrical conductivity to be satisfied the physical phenomena of the problem. Both methods are in very good agreement with the exact solutions.