Discretization of fractional boundary value problems using split operator local extension problems
| Autor: | John Paul Roop |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Numerical Analysis
Partial differential equation Discretization Applied Mathematics Finite difference 010103 numerical & computational mathematics 01 natural sciences 010101 applied mathematics Computational Mathematics Nonlinear system Operator (computer programming) Neumann boundary condition Meshfree methods Applied mathematics Boundary value problem 0101 mathematics Mathematics |
| Zdroj: | Applied Numerical Mathematics. 152:267-274 |
| ISSN: | 0168-9274 |
| Popis: | Partial differential equations which include nonlocal operators have recently become a major focus of mathematical and computational research. The efficient computational implementation of a nonlocal operator remains an important question. In this article, we introduce an operator splitting approach to the discretization of nonlocal boundary value problems. It has been shown that the fractional Laplacian in R d is identical to equivalent local extension problem in R d + 1 with a nonlinear Neumann boundary condition. We present an operator splitting approach to the extended problem that enables a consistent stable implementation. Computational experiments are presented using finite differences and meshless methods. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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