Numerical solution of nonlinear system of Klein–Gordon equations by cubic B-spline collocation method

Abstract

A technique to approximate the solutions of nonlinear Klein–Gordon equation and Klein–Gordon-Schrödinger equations is presented separately. The approach is based on collocation of cubic B-spline functions. The above-mentioned equations are decomposed into a system of partial differential equations, which are further converted to an amenable system of ODEs. The obtained system has been solved by SSP-RK54 scheme. Numerical solutions are presented for five examples, to show the accuracy and usefulness of proposed approach. The approximate solutions of both the equations are computed without using any transformation and linearization. The technique can be applied with ease to solve linear and nonlinear PDEs and also reduces the computational work.

Keywords:

• Klein–Gordon equation
• coupled Klein–Gordon–Schrödinger equations
• Thomas algorithm
• modified cubic B-spline basis function
• SSP-RK54 scheme

2010 AMS Subject Classifications::

• 65N30
• 74S05
• 65D07
• 65N35

Acknowledgements

The authors thank the anonymous referees for their time, efforts and valuable comments to improve the quality of the manuscript.