The application of cubic trigonometric B-spline to the numerical solution of time-fractional telegraph equation
This work provides an incremental improvement in numerical methods for solving fractional partial differential equations, offering a more accurate scheme for researchers in applied mathematics and engineering.
The paper proposes a numerical method for the time-fractional telegraph equation using cubic trigonometric B-splines and finite differences, demonstrating improved accuracy over existing techniques through stability analysis and computational experiments.
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.