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 L1/L2 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 $\mathcal{O}(\delta_t^{3-\alpha})$ 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.
Dabiri, S. M., & Damirchi, J. (2026). A Hybrid Numerical Scheme for the Time-Fractional Telegraph Equation. Analytical and Numerical Solutions for Nonlinear Equations, (), -. doi: 10.22128/ansne.2026.3271.1201
MLA
Seyyedeh Mitra Dabiri; Javad Damirchi. "A Hybrid Numerical Scheme for the Time-Fractional Telegraph Equation", Analytical and Numerical Solutions for Nonlinear Equations, , , 2026, -. doi: 10.22128/ansne.2026.3271.1201
HARVARD
Dabiri, S. M., Damirchi, J. (2026). 'A Hybrid Numerical Scheme for the Time-Fractional Telegraph Equation', Analytical and Numerical Solutions for Nonlinear Equations, (), pp. -. doi: 10.22128/ansne.2026.3271.1201
VANCOUVER
Dabiri, S. M., Damirchi, J. A Hybrid Numerical Scheme for the Time-Fractional Telegraph Equation. Analytical and Numerical Solutions for Nonlinear Equations, 2026; (): -. doi: 10.22128/ansne.2026.3271.1201
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