An Unconditionally Stable Method for Solving the Heat Conduction Equation Using Laguerre Polynomials

Abstract

In this work, an unconditionally stable method for solving the heat conduction equation is proposed. In the equation, the temperature field and its first order time derivatives are expanded by the Laguerre polynomials and weighting functions. By applying a Galerkin temporal testing procedure to the finite difference format, the time-step limitation can be eliminated in the process of computation and one can obtain an equation under no convergent conditions. To verify the efficiency and the accuracy of this presented method, we compare the numerical results of the presented method with the finite difference method (FDM) and the alternating direction implicit (ADI) method. The comparison results show that the proposed method has great advantage in efficiency while maintaining high accuracy when solving a heat transfer problem in a complex media with fine structure.