10ème JEAN, 20 décembre 2012
Katharina Schratz
:
Asymptotic preserving schemes for the non-relativistic Klein-Gordon equation.
We consider the Klein-Gordon equation in the non-relativistic limit regime, i.e. the speed of light c tending to infinity. The numerical simulation of this equation is highly delicate as even Gautschi methods which are numerical methods especially adjusted to highly-oscillatory problems require time steps of order 1/c^2. Here we will study the asymptotic expansion of the exact solution in terms of 1/c^2 and show that the first terms of this asymptotic can easily be simulated. Thus, this new approach allows us to construct numerical schemes which don't need to obey any c-dependent time step restriction.
This is a joint work with Erwan Faou.
