Three stories of high oscillation (Q389895)

From the introduction: High oscillation is present in a very wide range of phenomena and numerical modelling of high-frequency phenomena is vital. Yet, the Taylor theorem alone is inadequate for this purpose, calling for an entirely new breed of discretization methods. One such type of methods endeavours to bring together numerical analysis and asymptotic expansions, marrying local behaviour with global features of the solution. Three such scenarios are described: the computation of highly oscillatory integrals, the discretization of ordinary differential equations with highly oscillatory forcing terms and the computation of the linear Schrödinger equation. In none of these cases have we tried to achieve the greatest possible generality or sophistication, opting instead for accessible examples of numerical methods where global behaviour informs computation.