A Hybrid Numerical Scheme for the Time-Fractional Telegraph Equation

This study introduces a hybrid approach based on a finite difference scheme and radial basis functions (RBF) for solving the Caputo time-fractional telegraph equation numerically. To handle the temporal fractional derivatives, a finite difference formulation of the L۱/L۲ type is adopted, while the spatial derivatives are approximated using an RBF collocation technique. This combination results in a  discretized system characterized by a sparse matrix structure. Through the application of energy methods, the stability and convergence assessment of the temporal discretization is conducted, yielding a theoretical error estimate of \mathcal{O}(\delta_t^{۳-\alpha}) in the time direction. The reliability and effectiveness of the proposed numerical scheme are verified through a representative test problem, confirming the capability of the proposed method to achieve high accuracy.

کلیدواژه ها:

Time–fractional telegraph equation ، Caputo derivative ، Collocation method ، Radial basis functions ، Stability and convergence