An efficient numerical technique for the solution of nonlinear heat equation via spectral method

摘要

Nonlinear wave equations are more difficult to study mathematically, and no general analytical method exists for their solution. It is found that the Exponential Time Differencing (ETD) scheme requires the steps to achieve a given accuracy, offers a speedy method in calculation time, and has exceptional stability properties in solving a nonlinear equation. This article solves the diagonal example of nonlinear heat equation via the exponential time difference Runge-Kutta 4 methods (ETDRK4). Implementation of the method is proposed by short Matlab programs.