首页|Second order scheme for self-similar solutions of a time-fractional porous medium equation on the half-line

Second order scheme for self-similar solutions of a time-fractional porous medium equation on the half-line

扫码查看
原文链接
  • NSTL
  • Elsevier
Many physical, biological, and economical systems exhibit various memory effects due to which their present state depends on the history of the whole evolution. Combined with the nonlinearity of the process these phenomena pose serious difficulties in both analytical and numerical treatment. We investigate a time-fractional porous medium equation that has proved to be important in many applications, notably in hydrology and material sciences. We show that solutions of the free boundary Dirichlet, Neumann, and Robin problems on the half-line satisfy a Volterra integral equation with a non-Lipschitz nonlinearity. Based on this result we prove existence, uniqueness, and construct a family of numerical methods that solve these equations outperforming the usual finite difference approach. Moreover, we prove the convergence of these methods and support the theory with several numerical examples. (C) 2022 Elsevier Inc. All rights reserved.

Numerical methodPorous medium equationAnomalous diffusionFractional derivativeVolterra equationNon-LipschitzFINITE-DIFFERENCE METHODANOMALOUS DIFFUSIONINTEGRAL-EQUATIONSRICHARDS EQUATIONWATER TRANSPORTAPPROXIMATIONSTABILITYCONVERGENCEPROFILESDYNAMICS

Okrasinska-Plociniczak, Hanna、Plociniczak, Lukasz

展开 >

Wroclaw Univ Environm & Life Sci

Wroclaw Univ Sci & Technol

2022

10.1016/j.amc.2022.127033

Applied mathematics and computation

Applied mathematics and computation

EISCI
ISSN：0096-3003
年,卷(期)：2022.424
  • 4
  • 78