Reduced model-based parareal simulations of oscillatory singularly perturbed ordinary differential equations

We propose a new strategy for solving by the parareal algorithm highly oscillatory ordinary differential equations which are characteristics of six-dimensional Vlasov equation. For coarse solvers we use reduced models, obtained from two-scale asymptotic expansions in [4]. Such models have low computational cost since they free high oscillations. The method allows to improve their accuracy few iterations through corrections fine full model. demonstrate and efficiency numerical experiments short time long simulations charged particles submitted large magnetic field. In addition, convergence is uniformly with respect vanishing stiff parameter.