Jitse Niesen
Research interests
At the moment, I am mainly pursuing two topics for
research: geometric integration and the numerical evaluation of the
Evans function.
Geometric integration is concerned with the construction of
numerical algorithms which preserve some of the dynamical properties
of the exact solution. Examples of geometric integration methods that
I am studying include Magnus methods and exponential integrators.
The Evans function can be used as a tool to analyse the
stability of coherent structures for partial differential
equations. I am particularly interested in the stability of
travelling wave solutions for systems of reaction–diffusion
equations, like the Gray–Scott model. The main questions here are
how to efficiently evaluate the Evans function, and how to treat
two-dimensional problems.
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