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[quad] Implement methods from Li2020 #21

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alexfikl opened this issue Sep 4, 2023 · 1 comment
Open

[quad] Implement methods from Li2020 #21

alexfikl opened this issue Sep 4, 2023 · 1 comment
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enhancement New feature or request help wanted Extra attention is needed

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@alexfikl
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alexfikl commented Sep 4, 2023

Li2020 contains a fairly up to date set of numerical methods for fractional derivatives and integrals.
It would be very cool to implement most of this and compare.

  • Chapter 3: Riemann-Liouville quadrature
    • ✔️ 3.1.I: Fractional rectangular rule
    • ✔️ 3.1.II: Fractional trapezoidal rule
    • ✔️ 3.1.III: Fractional Simpson's rule
    • 3.1.IV: Fractional Newton-Cotes rules
    • ❔ 3.1.V: Cubic Hermitian interpolation rules
    • ❔ 3.2: Fractional multistep methods
    • ✔️ 3.3.I: Spectral approximations with Jacobi polynomials
    • ❔ 3.3.II: Spectral approximations with Legendre polynomials
      • Already works for Jacobi with $\alpha = \beta = 0$.
    • ❔ 3.3.III: Spectral approximations with Chebyshev polynomials
      • Already works for Jacobi with $\alpha = \beta = -1/2$.
    • ❔ 3.4: Diffusive approximations
@alexfikl alexfikl changed the title [general] Implement methods from Li2020 [quad|diff] Implement methods from Li2020 Sep 4, 2023
@alexfikl alexfikl changed the title [quad|diff] Implement methods from Li2020 [quad] Implement methods from Li2020 Sep 4, 2023
@alexfikl alexfikl added enhancement New feature or request help wanted Extra attention is needed labels Sep 4, 2023
@alexfikl
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alexfikl commented Sep 5, 2023

Generic Newton-Cotes is quite hard to implement (Li2020 doesn't give any details) since we can't nicely integrate arbitrary order Lagrange polynomials.

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