A symmetric fractional-order reduction method for direct nonuniform approximations of semilinear diffusion-wave equations [article]

Pin Lyu, Seakweng Vong
2021 arXiv   pre-print
We introduce a symmetric fractional-order reduction (SFOR) method to construct numerical algorithms on general nonuniform temporal meshes for semilinear fractional diffusion-wave equations. By using the novel order reduction method, the governing problem is transformed to an equivalent coupled system, where the explicit orders of time-fractional derivatives involved are all α/2 (1<α<2). The linearized L1 scheme and Alikhanov scheme are then proposed on general time meshes. Under some reasonable
more » ... regularity assumptions and weak restrictions on meshes, the optimal convergence is derived for the two kinds of difference schemes by H^2 energy method. An adaptive time stepping strategy which based on the (fast linearized) L1 and Alikhanov algorithms is designed for the semilinear diffusion-wave equations. Numerical examples are provided to confirm the accuracy and efficiency of proposed algorithms.
arXiv:2101.09678v3 fatcat:eyidssjtejcs3a3hew2sbarthy