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Pathfollowing for essentially singular boundary value problems with application to the complex Ginzburg–Landau equation (2009)
| Content Provider | CiteSeerX |
|---|---|
| Author | Kitzhofer, Georg Koch, Othmar |
| Abstract | We discuss a pathfollowing strategy based on pseudo-arclength parametrization for the solution of parameter-dependent boundary value problems for ordinary differen-tial equations. We formulate criteria which ensure the successful application of this method for the computation of solution branches with turning points for problems with an essential singularity. Finally, we demonstrate that a Matlab implementation of the solution method based on an adaptive collocation scheme is well suited to solve problems of practical relevance. As one example, we compute solution branches for the complex Ginzburg-Landau equation which start from multi-bump solutions of the nonlinear Schrödinger equation. Following the branches around turning points, real-valued solutions of the nonlinear Schrödinger equation can easily be computed. Key words: Boundary value problems for ordinary differential equations, essential singularity, pathfollowing strategy, pseudo-arclength parametrization, turning point, nonlinear Schrödinger equation, complex Ginzburg-Landau equation, self-similar blow-up solutions, collocation methods |
| File Format | |
| Journal | BIT |
| Language | English |
| Publisher Date | 2009-01-01 |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
