A high-order unconditionally stable scheme for time-fractional telegraph equations with generalized alternating numerical fluxes: Analysis and properties

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Abstract

This paper introduces and examines a flexible numerical strategy for solving the time-fractional telegraph equation. A finite difference scheme is used for temporal discretization, while spatial discretization is achieved using a discontinuous Galerkin method that incorporates generalized alternating numerical fluxes. From an implementation standpoint, these generalized alternating fluxes offer enhanced flexibility and greater adaptability compared with conventional flux selections. We prove that the resulting numerical scheme is unconditionally stable and convergent. Several numerical examples are provided to demonstrate the robustness, reliability, and accuracy of the proposed method.

Keywords

fractional calculus / numerical scheme / generalized alternating numerical fluxes / stability

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