Electronic Research Archive (Jan 2024)
An implicit fully discrete compact finite difference scheme for time fractional diffusion-wave equation
Abstract
In this paper, an implicit compact finite difference (CFD) scheme was constructed to get the numerical solution for time fractional diffusion-wave equation (TFDWE), in which the time fractional derivative was denoted by Caputo-Fabrizio (C-F) sense. We proved that the full discrete scheme is unconditionally stable. We also proved that the rate of convergence in time is near to $ O(\tau^{2}) $ and the rate of convergence in space is near to $ O(h^{4}) $. Test problem was considered for regular domain with uniform points to validate the efficiency and accuracy of the method. The numerical results can support the theoretical claims.
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