numerical-mathematics / extrapolation

Parallel extrapolation for ODEs
MIT License
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Automatic start step #9

Open mcr222 opened 8 years ago

mcr222 commented 8 years ago

Add an initial step algorithm that chooses with which step to start the solver. Currently initial step, if not specified, is 0.5. This step, for stiff problems, is usually too large.

When the step is too large, it usually causes an overflow of the RHS function. When that happens the new step is reduced by the robustness factor (as new step can't by estimated with the work estimation).

This behaviour is correct, but when the starting step is too large it means that a lot of steps are taken at the beginning to reach a good step size. This could be solved with an automatic initial step algorithms. See II.4 Starting step size. pg 169 Solving Ordinary Differential Equations I.