Collocation and finite difference-collocation methods for the solution of nonlinear Klein–Gordon equation

Two numerical techniques based on the finite difference and collocation methods are presented for the solution of nonlinear Klein–Gordon equation. The operational matrix of derivative for the cubic B-spline scaling functions is presented and is utilized to reduce the solution of nonlinear Klein–Gordon equation to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the new techniques.