AN EFFICIENT HYBRID B-SPLINE APPROACH FOR NUMERICAL APPROXIMATION OF TIME-FRACTIONAL TELEGRAPH EQUATIONS

Abstract

Telegraph equations are hyperbolic partial differential equations that display diffusion reaction processes in a biological and engineering field. The main purpose of this work is to solve time fractional telegraph equation using spline functions especially the application of Hybrid cubic B-spline (HCBS) functions. The proposed method utilizes HCBS functions to interpolate the solution curve over the spatial grid, while the time fractional derivative is discretized using the Caputo fractional derivative formula. The basic objective of the study is to developed a numerical solution for an initial boundary value issue by using finite difference methods for a hyperbolic equation. Accordingly, this study introduces a method based on finite difference formulas and time-frequency analysis to address initial boundary value problems. The stability and convergence of the approach are established through conventional analytical methods, confirming that the scheme is unconditionally stable and exhibits a specific convergence rate. To validate the theoretical results, various numerical experiments are carried out. Additionally, the plotted results demonstrate a strong correlation between the exact and computed solutions, highlighting the precision of the technique.