The goal of the project is to develop and analyse numerical methods for computing moving patterns in time dependent partial differential equations. Examples are traveling waves in one, spiral waves in two, and scroll waves in three space dimensions. These occur in reaction diffusion systems and (non) viscous conservation laws that are equivariant with respect to the action of a Lie group. Our focus is the {\it freezing method\/} that allows to compute adaptive coordinate frames in which patterns become stationary. We investigate nonlinear stability of patterns, its relation to spectral properties, the influence of random perturbations, and we extend the method to handle multiple patterns.
| 13020 | Stability and Computation of Dynamic Patterns in PDEs | PDF | PS.GZ |
| 12139 | Spatial decay of rotating waves in parabolic systems | PDF | PS.GZ |
| 12099 | Finding eigenvalues of holomorphic Fredholm operator pencils using boundary value problems and contour integrals | PDF | PS.GZ |
| 12097 | Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients | PDF | PS.GZ |
| 12096 | Convergence of the stochastic Euler scheme for locally Lipschitz coefficients | PDF | PS.GZ |
| 12040 | A numerical method for the solution of relaxed one-sided Lipschitz algebraic inclusions | PDF | PS.GZ |
| 12023 | Computing covariant vectors, Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study | PDF | PS.GZ |
| 12005 | Stability of parabolic-hyperbolic traveling waves | PDF | PS.GZ |
| 11117 | Continuation and collapse of homoclinic tangles | PDF | PS.GZ |
| 11079 | Stability and Freezing of Waves in Nonlinear Hyperbolic-Parabolic Systems | PDF | PS.GZ |
