Second order scheme for self-similar solutions of a time-fractional porous medium equation on the half-line
作者：
Highlights：
• An efficient numerical method for solving time-fractional porous medium equation on the half-line with self-similar boundary conditions is devised and analyzed.
• The second order method stems from the discretization of the nonlinear Volterra equation and converges to the nontrivial solution.
• Numerical simulations and computational complexity estimates indicate that the method is superior to the finite difference scheme.
摘要
•An efficient numerical method for solving time-fractional porous medium equation on the half-line with self-similar boundary conditions is devised and analyzed.•The second order method stems from the discretization of the nonlinear Volterra equation and converges to the nontrivial solution.•Numerical simulations and computational complexity estimates indicate that the method is superior to the finite difference scheme.
论文关键词：Numerical method,Porous medium equation,Anomalous diffusion,Fractional derivative,Volterra equation,Non-Lipschitz
论文评审过程：Received 28 September 2021, Revised 7 February 2022, Accepted 15 February 2022, Available online 26 February 2022, Version of Record 26 February 2022.
论文官网地址：https://doi.org/10.1016/j.amc.2022.127033
