Name
Title | ||
|---|---|---|
Parameter-robust numerical method for a system of singularly perturbed initial value problems |
Abstract | ||
|---|---|---|
In this work we study a system of M(驴驴驴2) first-order singularly perturbed ordinary differential equations with given initial conditions. The leading term of each equation is multiplied by a distinct small positive parameter, which induces overlapping layers. A maximum principle does not, in general, hold for this system. It is discretized using backward Euler difference scheme for which a general convergence result is derived that allows to establish nodal convergence of O(N 驴驴驴1ln N) on the Shishkin mesh and O(N 驴驴驴1) on the Bakhvalov mesh, where N is the number of mesh intervals and the convergence is robust in all of the parameters. Numerical experiments are performed to support the theoretical results. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1007/s11075-011-9483-4 | Numerical Algorithms |
Keywords | Field | DocType |
Singular perturbation,Initial-value problem,Layer-resolving meshes,Parameter-robust convergence | Convergence (routing),Discretization,Mathematical optimization,Maximum principle,Ordinary differential equation,Mathematical analysis,Singular perturbation,Initial value problem,Numerical analysis,Backward Euler method,Mathematics | Journal |
Volume | Issue | ISSN |
59 | 2 | 1017-1398 |
Citations | PageRank | References |
3 | 0.51 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Sunil Kumar | 1 | 86 | 10.07 |
| Mukesh Kumar | 2 | 9 | 1.85 |