3 ms·
> The Chebyshev basis is much better The Chebyshev basis in time is still not great. This was used in Chebfun before but there's a note that for time to just u
by ChrisRackauckas 4y ago
> The Chebyshev basis is much better
The Chebyshev basis in time is still not great. This was used in Chebfun before but there's a note that for time to just use standard ODE solvers because it did not good performance. Collocation really only makes sense on BVPs.
- mturmon 4y agoThis comment and GP comment open up a helpful learning experience for a casual/occasional user like me. This distinction between initial value problems (IVP, one endpoint known, hence a “time” differential equation) and BVPs (both endpoints known, not “time”) also appears in this introduction to the Chebfun solvers: https://www.chebfun.org/docs/guide/guide07.html https://www.chebfun.org/docs/guide/guide07.html (last paragraph of sec 7.1) Following the breadcrumbs to the IVP treatment in chapter 10 https://www.chebfun.org/docs/guide/guide10.html https://www.chebfun.org/docs/guide/guide10.html (Sec 10.2) we read: A major change was introduced in Version 5.1 in how initial-value (and final-value) problems are solved. Before, Chebfun used the same global spectral representations as for BVPs. This usually works fine for linear problems, but for nonlinear ones, it is inferior to the method of time-stepping by Runge-Kutta or Adams formulas. In Chebfun Version 5.1, we accordingly switched to solving IVPs numerically by ode113 (by default), converting the resulting output to a Chebfun representation. Thanks again for the helpful comments.