Name
Title | ||
|---|---|---|
On the uniform convergence of a finite difference scheme for time dependent singularly perturbed reaction-diffusion problems |
Abstract | ||
|---|---|---|
In this work we are interested in the numerical approximation of 1D parabolic singularly perturbed problems of reaction-diffusion type. To approximate the multiscale solution of this problem we use a numerical scheme combining the classical backward Euler method and central differencing. The scheme is defined on some special meshes which are the tensor product of a uniform mesh in time and a special mesh in space, condensing the mesh points in the boundary layer regions. In this paper three different meshes of Shishkin, Bahkvalov and Vulanovic type are used, proving the uniform convergence with respect to the diffusion parameter. The analysis of the uniform convergence is based on a new study of the asymptotic behavior of the solution of the semidiscrete problems, which are obtained after the time discretization by the Euler method. Some numerical results are showed corroborating in practice the theoretical results on the uniform convergence and the order of the method. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1016/j.amc.2010.02.050 | Applied Mathematics and Computation |
Keywords | Field | DocType |
parabolic reaction–diffusion problems,special nonuniform mesh,parabolic reaction-diffusion problems,uniform convergence,semidiscrete problems,asymptotic behavior,boundary layer,tensor product,reaction diffusion | Discretization,Mathematical optimization,Euler method,Mathematical analysis,Uniform convergence,Asymptotic analysis,Backward Euler method,Reaction–diffusion system,Mathematics,Parabola,Modes of convergence | Journal |
Volume | Issue | ISSN |
216 | 5 | Applied Mathematics and Computation |
Citations | PageRank | References |
6 | 0.90 | 5 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| C. Clavero | 1 | 114 | 22.46 |
| J. L. Gracia | 2 | 139 | 18.36 |