A convergent exponential B-spline collocation method for a time-fractional telegraph equation

Abstract

This work aims to develop and analyze a numerical method for solving a time-fractional telegraph equation of Caputo type. The method is constructed using a finite difference method for the time discretization and exponential B-spline functions for the space discretization. The unique solvability is well demonstrated. The convergence of the method is discussed in detail and the proposed method is shown to be convergent with the convergence order O(h2, Δ t) , where h and Δ t represent mesh sizes in the space and time directions, respectively. The proposed numerical method is employed on two test problems, and their results have manifested the eminence and validity of our approach. © 2023, The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional.