A new numerical method for solving the heat conduction equation in one dimensional nanometer materials

摘要

In order to obtain the numerical solution of the heat conduction equation in one dimensional nanometer materials, we discrete the demand equation by Galerkin-Legendre spectral method and obtain a system of order ordinary differential equations, then we solve this system by using a fifth order five stage A-stable new diagonally implicit Runge-Kutta method. Numerical results are presented to demonstrate the accuracy and efficiency of this method.