Abstract
In this work, an efficient alternating direction implicit (ADI) finite difference scheme is proposed to solve the three-dimensional time-fractional telegraph equation. The fully-discrete scheme is established via the L1 discrete formula in temporal direction and finite difference method in spatial direction. In order to reduce the computational cost of solving three-dimensional problems, an ADI algorithm is designed and applied. Then, via the energy method, we prove the stability and convergence of the scheme in L2 and H1 norms, respectively. Eventually, several numerical examples are given to validate the theoretical results.
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