Preprint Article Version 1 NOT YET PEER-REVIEWED

Trigonometric Cubic B-spline Collocation Method for Solitons of the Klein-Gordon Equation

Version 1 : Received: 1 December 2016 / Approved: 2 December 2016 / Online: 2 December 2016 (08:45:07 CET)

How to cite: Korkmaz, A.; Ersoy, O.; Dag, I. Trigonometric Cubic B-spline Collocation Method for Solitons of the Klein-Gordon Equation. Preprints 2016, 2016120013 (doi: 10.20944/preprints201612.0013.v1). Korkmaz, A.; Ersoy, O.; Dag, I. Trigonometric Cubic B-spline Collocation Method for Solitons of the Klein-Gordon Equation. Preprints 2016, 2016120013 (doi: 10.20944/preprints201612.0013.v1).

Abstract

In the present study, we derive a new B-spline technique namely trigonometric B-spline collocation algorithm to solve some initial boundary value problems for the nonlinear Klein-Gordon equation. In order to carry out the time integration with Crank-Nicolson implicit method, the order of the equation is reduced to give a coupled system of nonlinear partial differential equations. The collocation approximation based on trigonometric cubic B-splines for spatial discretization is followed by the linearization of the nonlinear term. The efficiency and accuracy of the present method are validated by measuring the error between the numerical and analytical solutions when exist. The conservation laws representing momentum and energy are also computed for all problems.

Subject Areas

Klein-Gordon equation; trigonometric cubic B-spline; collocation; soliton; wave motion; conservation laws

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