The application of cubic trigonometric B-spline to the numerical solution of time-fractional telegraph equation

TL;DR

This paper introduces a novel numerical method using cubic trigonometric B-splines for solving the time-fractional telegraph equation, demonstrating improved accuracy and stability over existing techniques.

Contribution

It develops a new finite difference scheme combining cubic trigonometric B-splines with Caputo derivatives for enhanced numerical solutions.

Findings

The scheme is stable and error does not amplify.

Numerical results outperform existing methods.

The method is efficient and more accurate.

Abstract

In this paper, an efficient numerical technique for the time-fractional telegraph equation is proposed. The aim of this paper is to use a relatively new type of B-spline called the cubic trigonometric B-splines for the proposed scheme. This technique is based on finite difference formulation for the Caputo time-fractional derivative and cubic trigonometric B-splines based technique for the derivatives in space. A stability analysis of the scheme is set up to affirm that the errors do not amplify. Computational experiments are carried out in addition to verify the theoretical analysis. Numerical results are compared with some existing techniques and it is concluded that the present scheme is more accurate and effective.