A local meshless method to approximate the time-fractional telegraph equation

Abstract

In the present work, we investigate the numerical solution of time-fractional telegraph equation by a local meshless method. The fractional-order derivative is defined in the Caputo’s sense. The time semi-discretization was carried out using finite difference method followed by radial basis function-based spatial discretization. The theoretical convergence analysis and stability analysis of time semi-discrete scheme are also proved. Several test problems with regular and irregular domains with uniform and non-uniform points are considered. To demonstrate the accuracy and efficiency of the proposed method, we compared the analytical and numerical solution of the proposed problem.