Name
Title | ||
|---|---|---|
Analysis of a New Error Estimate for Collocation Methods Applied to Singular Boundary Value Problems |
Abstract | ||
|---|---|---|
We discuss an a posteriori error estimate for the numerical solution of boundary value problems for nonlinear systems of ordinary differential equations with a singularity of the first kind. The estimate for the global error of an approximation obtained by collocation with piecewise polynomial functions is based on the defect correction principle. We prove that for collocation methods which are not superconvergent, the error estimate is asymptotically correct. As an essential prerequisite we derive convergence results for collocation methods applied to nonlinear singular problems. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1137/S0036142902418928 | SIAM J. Numerical Analysis |
Keywords | DocType | Volume |
singular boundary value problems,collocation method,new error estimate,boundary value problems,error estimate,global error,essential prerequisite,defect correction principle,posteriori error estimate,collocation methods applied,nonlinear system,defect correction,convergence result,singularity of the first kind,boundary value problem,numerical solution,asymptotical correctness.,collocation methods | Journal | 42 |
Issue | ISSN | Citations |
6 | 0036-1429 | 12 |
PageRank | References | Authors |
1.85 | 5 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Winfried Auzinger | 1 | 56 | 10.48 |
| Othmar Koch | 2 | 174 | 28.41 |
| Ewa Weinmüller | 3 | 118 | 24.75 |