Name
Abstract | ||
|---|---|---|
Differentialalgebraic equations with higher index give rise to essentially ill-posed problems. Therefore, their numerical approximation requires special care. In the present paper, we state the notion of ill-posedness for linear differentialalgebraic equations more precisely. Based on this property, we construct a regularization procedure using a least-squares collocation approach by discretizing the pre-image space. Numerical experiments show that the resulting method has excellent convergence properties and is not much more computationally expensive than standard collocation methods used in the numerical solution of ordinary differential equations or index-1 differentialalgebraic equations. Convergence is shown for a limited class of linear higher-index differentialalgebraic equations. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1016/j.cam.2016.12.017 | J. Computational Applied Mathematics |
Keywords | Field | DocType |
Differential–algebraic equation,Higher index,Essentially ill-posed problem,Collocation,Boundary value problem,Initial value problem | Numerical methods for ordinary differential equations,Mathematical optimization,Exponential integrator,Orthogonal collocation,Mathematical analysis,Numerical partial differential equations,Backward differentiation formula,Collocation method,Independent equation,Numerical stability,Mathematics | Journal |
Volume | Issue | ISSN |
317 | C | 0377-0427 |
Citations | PageRank | References |
1 | 0.48 | 2 |
Authors | ||
5 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Michael Hanke | 1 | 6 | 4.19 |
| Roswitha März | 2 | 25 | 10.56 |
| C. Tischendorf | 3 | 80 | 15.62 |
| Ewa Weinmüller | 4 | 118 | 24.75 |
| Stefan Wurm | 5 | 1 | 0.48 |