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Composition methods for differential equations with processing
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DOI：10.1137/030601223.png)
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摘要
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We construct numerical integrators for differential equations up to order 12 obtained by composition of basic integrators. The following cases are considered: ( i) composition for a system separable in two solvable parts, ( ii) composition using as basic methods a first-order integrator and its adjoint, ( iii) composition using second-order symmetric methods, and ( iv) composition using fourth-order symmetric methods. Each scheme is implemented with a processor or corrector to improve their efficiency, and this can be done virtually cost-free.
Keyword:
composition methods
geometric integrators
processing technique
cheap postprocessor
initial value problems