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B-Methods: Geometric Integrators for Blowup Problems

Banff International Research Station for Mathematical Innovation and Discovery

Time dependent nonlinear partial differential equations, like for example reaction diffusion equations, are usually solved by classical time marching schemes, like Runge-Kutta methods, or linear multi-step methods. Such equations can however have solutions which blow up in finite time, and in the blowup regime, the behavior of the solution is dominated by the non-linearity. I will show two different approaches how one can construct specialized numerical time integrators which take into account the physics of the underlying non-linear problem. I will show both theoretically and numerically that their performance can be orders of magnitude better than the performance of classical time integrators for such problems.

Mathematics; Numerical analysis

video/mp4

Author affiliation: Université de Genève

2017-12-10

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63880

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/