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Improve Caputo diffusive methods #50

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alexfikl opened this issue Jul 9, 2024 · 0 comments
Open

Improve Caputo diffusive methods #50

alexfikl opened this issue Jul 9, 2024 · 0 comments
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diff Changes to the differentiation module enhancement New feature or request

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@alexfikl
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alexfikl commented Jul 9, 2024

Currently, the diffusive methods for the Caputo derivative require to solve an ODE like

$$\phi'(\xi; \omega) = h(\omega) f^{(m)}(\xi) - g(\omega) \phi(\xi; \omega)$$

where we have the derivative of the function. This currently requires an analytic expression for the derivative, which is not great.. We should use some nice approximation.

This may require some custom ODE solver, so we can have control over the time steps at which to evaluate $f(\xi)$.

@alexfikl alexfikl added the enhancement New feature or request label Jul 9, 2024
@alexfikl alexfikl changed the title [diff] Improve Caputo diffusive methods Improve Caputo diffusive methods Dec 11, 2024
@alexfikl alexfikl added the diff Changes to the differentiation module label Dec 11, 2024
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Labels
diff Changes to the differentiation module enhancement New feature or request
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