Numerical Method for the Time-Fractional Porous Medium Equation
| Autor: | Łukasz Płociniczak |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Numerical Analysis
Applied Mathematics Numerical analysis Finite difference method Volterra equations Fractional calculus Computational Mathematics symbols.namesake Dirichlet boundary condition Scheme (mathematics) Convergence (routing) symbols Applied mathematics Mathematics - Numerical Analysis Porous medium Mathematics |
| Zdroj: | SIAM Journal on Numerical Analysis. 57:638-656 |
| ISSN: | 1095-7170 0036-1429 |
| DOI: | 10.1137/18m1192561 |
| Popis: | This papers deals with a construction and convergence analysis of a finite difference scheme for solving time-fractional porous medium equation. The governing equation exhibits both nonlocal and nonlinear behaviour making the numerical computations challenging. Our strategy is to reduce the problem into a single one-dimensional Volterra integral equation for the self-similar solution and then to apply the discretization. The main difficulty arises due to the non-Lipschitzian behaviour of the equation's nonlinearity. By the analysis of the recurrence relation for the error we are able to prove that there exists a family of finite difference methods that is convergent for a large subset of the parameter space. We illustrate our results with a concrete example of a method based on the midpoint quadrature. |
| Databáze: | OpenAIRE |
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