Name
Abstract | ||
|---|---|---|
A new method is developed by detecting the boundary layer of the solution of a singular perturbation problem. On the non-boundary layer domain, the singular perturbation problem is dominated by the reduced equation which is solved with standard techniques for initial value problems. While on the boundary layer domain, it is controlled by the singular perturbation. Its numerical solution is provided with finite difference methods, of which up to sixth order methods are developed. The numerical error is maintained at the same level with a constant number of mesh points for a family of singular perturbation problems. Numerical experiments support the analytical results. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1016/j.camwa.2007.09.011 | Computers & Mathematics with Applications |
Keywords | Field | DocType |
singular perturbation,non-boundary layer domain,singular perturbation problem,numerical error,stability,boundary layer domain,analytical result,initial value problem,differential equations,reduced equation,numerical experiment,numerical solutions,nonlinear singular perturbation problem,numerical solution,boundary layer,differential equation,finite difference method | Regular singular point,Poincaré–Lindstedt method,Mathematical optimization,Mathematical analysis,Singular solution,Singular perturbation,Singular boundary method,Method of fundamental solutions,Finite difference method,Mathematics,Numerical stability | Journal |
Volume | Issue | ISSN |
55 | 11 | Computers and Mathematics with Applications |
Citations | PageRank | References |
2 | 0.43 | 1 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Tzu-Chu Lin | 1 | 4 | 1.18 |
| David H. Schultz | 2 | 2 | 0.43 |
| Weiqun Zhang | 3 | 43 | 5.64 |