A new class of uniformly accurate numerical schemes for highly oscillatory evolution equations
This provides a general framework for solving stiff oscillatory problems across a wide range of regimes, benefiting computational scientists working on evolution equations.
The paper introduces a new methodology for designing uniformly accurate numerical schemes for highly oscillatory evolution equations, achieving high-order approximations with errors and costs independent of the oscillation regime.
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.