Timeline for Do the Euler method's approximations always approach the true solution?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 24, 2011 at 17:39 | answer | added | Nilima Nigam | timeline score: 2 | |
| Oct 3, 2010 at 18:08 | vote | accept | CommunityBot | ||
| Oct 1, 2010 at 15:07 | answer | added | Dick Palais | timeline score: 10 | |
| Oct 1, 2010 at 4:01 | comment | added | Ryan Budney | I believe it's more or less a straight-forward exercise to deduce these types of results from the Gronwall inequality (stated in suitable generality) -- thinking of the Euler method as an exact solution to an approximation to the differential equation. So that might be a better thing to look for. | |
| Oct 1, 2010 at 3:58 | comment | added | Ryan Budney | Hubbard's TAM textbook "Differential Equations: A Dynamical Systems Approach. Part II: Higher Dimensional Systems" covers convergence of Euler's method for piecewise-linear approximating functions as you call them. He's dealing with finite-dimensional systems but the proof generalizes, of course. I imagine there are some more modern numerical analysis texts out there that would be a more comprehensive reference but that's off the top of my head. | |
| Oct 1, 2010 at 1:47 | history | asked | user5810 | CC BY-SA 2.5 |