Compact scheme for fractional diffusion-wave equation with spatial variable coefficient and delays. Issue 6 (13th April 2022) - Zhang, Qifeng; Liu, Lingling; Zhang, Chengjian
ABSTRACT: In this paper, we study the spatial variable coefficient fractional convection–diffusion wave equation with the singe delay and multi-delay numerically when the exact solution satisfies a certain regularity. First, via the well-known exponential transformation, the delay problem can be greatly simplified, which allows us to use the variable coefficient four-order compact operator. Next, the numerical scheme is derived based on the compact operator and the reduction order method, followed by a linearized technique. Convergence of the full discrete numerical scheme is obtained with convergence order O ( τ 3 − α + h 4 ) under the maximum norm by the energy argument. We prove the almost unconditional stability of the scheme under very mild conditions. Extending the numerical method to the multi-delay case is available. Extensive computational results are presented including single delay and double delay problems, which demonstrate the effectiveness and correctness of the developed schemes.