Radial basis function methods for the Rosenau equation and other higher order PDEs
| Autor: | Elisabeth Larsson, Ali Safdari-Vaighani, Alfa Heryudono |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Numerical Analysis
Applied Mathematics Mathematical analysis General Engineering Boundary (topology) Computational mathematics Numerical Analysis (math.NA) 010103 numerical & computational mathematics 01 natural sciences Theoretical Computer Science 010101 applied mathematics Computational Mathematics Computational Theory and Mathematics Rate of convergence 65M70 (Primary) 35G31 (Secondary) Collocation method Convergence (routing) FOS: Mathematics Meshfree methods Boundary value problem Mathematics - Numerical Analysis 0101 mathematics Software Mathematics Numerical partial differential equations |
| Popis: | Meshfree methods based on radial basis function (RBF) approximation are of interest for numerical solution of partial differential equations because they are flexible with respect to the geometry of the computational domain, they can provide high order convergence, they are not more complicated for problems with many space dimensions and they allow for local refinement. The aim of this paper is to show that the solution of the Rosenau equation, as an example of an initial-boundary value problem with multiple boundary conditions, can be implemented using RBF approximation methods. We extend the fictitious point method and the resampling method to work in combination with an RBF collocation method. Both approaches are implemented in one and two space dimensions. The accuracy of the RBF fictitious point method is analyzed partly theoretically and partly numerically. The error estimates indicate that a high order of convergence can be achieved for the Rosenau equation. The numerical experiments show that both methods perform well. In the one-dimensional case, the accuracy of the RBF approaches is compared with that of the corresponding pseudospectral methods, showing similar or slightly better accuracy for the RBF methods. In the two-dimensional case, the Rosenau problem is solved both in a square domain and in an irregular domain with smooth boundary, to illustrate the capability of the RBF-based methods to handle irregular geometries. |
| Databáze: | OpenAIRE |
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