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. (C) 2010 Elsevier B.V. All rights reserved.