Raising the order of geometric numerical integrators by composition and extrapolation
This paper deals with the construction of high order geometric integrators up to order sixteen. First, composition techniques are studied, the standard case, where one or more low order basic methods are composed, and the processing case, where one basic method of moderate order is composed with a post-processor method. Then the extrapolation technique for geometric integrators is analyzed. In general, the extrapolation doesn't preserve the geometric properties of the exact solution, but for most practical purposes, the preservation of the geometric properties they provide is sufficiently accurate. The interest of the integration schemes thus constructed is illustrated on the important class of differential equations \(y''=g(y,t)\) and the Schrödinger equation. Finally, several numerical examples are given.
scientific article; zbMATH DE number 2161200