Re:A lazy way to solve differential equations
by mturmon on Friday July 22, 2022 @02:58PM
(#32195816)
This 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:
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.
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 (last paragraph of sec 7.1)
Following the breadcrumbs to the IVP treatment in chapter 10
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.