Timeline for Why not evaluate integrals using ODE-solvers?
Current License: CC BY-SA 2.5
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| Nov 29, 2010 at 13:15 | comment | added | J. M. isn't a mathematician | Gauss-Legendre and Gauss-Lobatto tend to be used for "stiff" systems (in general, implicit methods are used for stiff systems); as a probably more familiar example, it can be shown that the usual fourth-order Runge-Kutta method, when applied to the ODE $y^{\prime}=f(x)$, is equivalent to using Simpson's rule on the integral of $f(x)$. Additionally, in general codes for adaptively solving ODEs tend to be more elaborate than adaptive quadrature codes, since as I said in the comment to Ricky's answer, one has to be more careful at extrapolating than interpolating. | |
| Nov 29, 2010 at 13:03 | history | answered | Jitse Niesen | CC BY-SA 2.5 |