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.

Jitse Niesen