A New Class of Uniformly Accurate Numerical Schemes for Highly Oscillatory Evolution Equations - Chartier, Philippe; Lemou, Mohammed; Méhats, Florian; Vilmart, Gilles (Foundations of computational mathematics, 2020)
We introduce a new methodology to design uniformly accurate methods for oscillatory evolution equations. The targeted models are envisaged in a wide spectrum of regimes, from non-stiff to highly oscillatory. Thanks to an averaging transformation, the stiffness of the problem is softened, allowing for standard schemes to retain their usual orders of convergence. Overall, high-order numerical approximations are obtained with errors and at a cost independent of the regime.