On the numerical solution of the Klein-Gordon equation by Exponential B-spline collocation method

TL;DR

This paper introduces an exponential B-spline collocation method for numerically solving the nonlinear Klein-Gordon equation, demonstrating its accuracy and ability to preserve conserved quantities.

Contribution

The paper develops a novel exponential B-spline collocation approach specifically for the Klein-Gordon equation, enhancing numerical solution accuracy and conservation property preservation.

Findings

The method achieves high accuracy compared to analytical solutions.

Conserved quantities are effectively preserved during simulations.

The approach is validated through error analysis and numerical experiments.

Abstract

In the present study, we solve initial boundary value problem construted on nonlinear Klein-Gordon equation. The collocation method on exponential cubic B-spline functions forming a set of basis for the functions defined in the same interval is set up for the numerical approach. The efficiency and validity of the proposed method are determined by computing the error between the numerical and the analytical solutions. The preservation of conserved quantities is also a good indicator of validity of the method.