Name
Title | ||
|---|---|---|
High order methods for elliptic and time dependent reaction-diffusion singularly perturbed problems |
Abstract | ||
|---|---|---|
The objective of this paper is to construct some high order uniform numerical methods to solve linear reaction-diffusion singularly perturbed problems. First, for 1D elliptic problems, based on the central finite difference scheme, a new HODIE method is defined on a piecewise uniform Shishkin mesh. Using this HODIE scheme jointly with a two stage SDIRK method, we solve a 1D parabolic singularly perturbed problem. In both cases we prove that the methods are third-order uniform convergent in the maximum norm. Finally, for a 2D parabolic problem of the same type, we show numerically that the combination of the HODIE scheme with a fractional step RK method gives again a third-order uniform convergent scheme. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1016/j.amc.2004.10.007 | Applied Mathematics and Computation |
Keywords | Field | DocType |
stage sdirk method,high order,piecewise uniform shishkin mesh,high order method,new hodie method,fractional step rk method,reaction–diffusion problems,third-order uniform convergent scheme,fractional rk method,time dependent reaction-diffusion singularly,uniform numerical method,sdirk method,uniform convergence,third-order uniform convergent,hodie schemes,elliptic problem,central finite difference scheme,hodie scheme,reaction diffusion,numerical method | Mathematical analysis,Uniform convergence,Finite difference method,Numerical analysis,Partial differential equation,Finite volume method,Elliptic curve,Piecewise,Mathematics,Parabola | Journal |
Volume | Issue | ISSN |
168 | 2 | Applied Mathematics and Computation |
Citations | PageRank | References |
13 | 2.42 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| C. Clavero | 1 | 114 | 22.46 |
| J. L. Gracia | 2 | 139 | 18.36 |