Name
Title | ||
|---|---|---|
Parameter-Uniform Numerical Methods for a Class of Singularity Perturbed Problems with a Neumann Boundary Condition |
Abstract | ||
|---|---|---|
The error generated by the classical upwind finite difference method on a uniform mesh, when applied to a class of singularly perturbed modelo rdinary differential equations with a singularly perturbed Neumann boundary condition, tends to infinity as the singular perturbation parameter tends to zero. Note that the exact solution is uniformly bounded with respect to the perturbation parameter. For the same classical finite difference operator on an appropriate piecewise-uniform mesh, it is shown that the numerical solutions converge, uniformly with respect to the perturbation parameter, to the exact solution of any problem from this class. |
Year | DOI | Venue |
|---|---|---|
2000 | 10.1007/3-540-45262-1_35 | NAA |
Keywords | Field | DocType |
classical upwind finite difference,exact solution,numerical solutions converge,appropriate piecewise-uniform mesh,singular perturbation parameter,parameter-uniform numerical methods,classical finite difference operator,neumann boundary condition,modelo rdinary differential equation,perturbation parameter,singularity perturbed problems,uniform mesh,numerical method,singular perturbation | Boundary value problem,Finite difference,Mathematical analysis,Uniform boundedness,Singular perturbation,Upwind scheme,Finite difference method,Neumann boundary condition,Numerical analysis,Mathematics | Conference |
Volume | ISSN | ISBN |
1988 | 0302-9743 | 3-540-41814-8 |
Citations | PageRank | References |
2 | 0.75 | 1 |
Authors | ||
5 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Paul A. Farrell | 1 | 38 | 7.52 |
| Alan F. Hegarty | 2 | 2 | 2.10 |
| John J. H. Miller | 3 | 5 | 3.12 |
| Eugene O'Riordan | 4 | 120 | 19.17 |
| Grigorii I. Shishkin | 5 | 52 | 15.80 |