Development of non polynomial spline and New B-spline with application to solution of Klein-Gordon equation

Document Type : Research Paper

Authors

1 Department of Mathematics and Statistics, Central Tehran Branch, Islamic Azad University, Tehran, Iran.

2 School of Mathematics, Iran University of Science and Technol- ogy, Hengam, Narmak, 168613114 Tehran, Iran.

Abstract

In this paper we develop a non polynomial cubic spline functions which we called ”TS spline”, based on trigonometric functions. The convergence analysis of this spline is investigated in details. The definition of B-spline basis function for TS spline is extended and ”TS B-spline” is introduced. This paper attempts to develop collocation method based on this B-spline for the numerical solution of the nonlinear Klein-Gordon equation. The convergence analysis of this approach is discussed, the second order of convergence is proved consequently. The proposed method is applied on some test examples and the numerical results are compared with those already available in literature. Observed errors in the solutions show the efficiency and numerical applicability of the proposed method.

Keywords

Computational Methods for Differential Equations
Volume 8, Issue 4
November 2020
Pages 794-814

Files

History

  • Receive Date: 10 June 2018
  • Revise Date: 05 August 2019
  • Accept Date: 25 August 2019

Share

How to cite

Statistics