Numerical Solution of the Nonlinear Wave Equation via Fourth-Order Time Stepping
Some nonlinear wave equations are more difficult to solve analytically. Exponential Time Differencing (ETD) technique requires minimum stages to obtain the required accurateness, which suggests an efficient technique relating to computational duration that ensures remarkable stability characteristics upon resolving the nonlinear wave equations. This article solves the non-diagonal example of Fisher equation via the exponential time differencing Runge-Kutta 4 method (ETDRK4). Implementation of the method is demonstrated by short Matlab programs.
Khanittha Wongseedakaew and Qi Luo
M. A. Lahiji and Z. A. Aziz, "Numerical Solution of the Nonlinear Wave Equation via Fourth-Order Time Stepping", Applied Mechanics and Materials, Vol. 729, pp. 213-219, 2015