Evaluation of mixed Crank–Nicolson scheme and Tau method for the solution of Klein–Gordon equation

摘要

Numerical method based on the Crank–Nicolson scheme and the Tau method is proposed for solving nonlinear Klein–Gordon equation. Nonlinear Klein–Gordon equation is reduced by Crank–Nicolson scheme to the system of ordinary differential equations then Tau method is used to solve this system by using interpolating scaling functions and operational matrix of derivative. The order of convergence is proposed and some numerical examples are included to demonstrate the validity and applicability of the technique. The method is easy to implement and produces accurate results.