Geometry of Numerical Complex Time Integration

Details Geometry of Numerical Complex Time Integration Geometry of Numerical Complex Time Integration

2009-03-09

arxiv.org/abs/0903.1585v1

Mathematics

Numerical Analysis

Scientific paper

We are studying Runge-Kutta methods along complex paths of integration from a geometric point of view. Thereby we derive special complex time grids, which applied to the problem of integrating a linear autonomous system of ordinary differential equations, can be used to achieve a classical superconvergence effect. The approach is also adapted for arbitrary ODEs. Furthermore we draw a connection from our geometric reasoning to the class of composition methods with complex coefficients. Thereby, our main goal is to introduce a new point of view on these methods.

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