Timeline for How to increase the speed of Collocation method to solve System of differential equations
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 28, 2021 at 13:48 | history | edited | xzczd♦ | CC BY-SA 4.0 |
speed up the code with AffineCovariantNewton method.
|
| May 28, 2021 at 13:24 | comment | added | Gummala Navneeth | @xzczd , Yes. thank you very much. | |
| May 28, 2021 at 12:55 | comment | added | xzczd♦ |
@GummalaNavneeth Do you mean something like uniform = Range[1., 21]; NDSolve`FiniteDifferenceDerivative[1, uniform, DifferenceOrder -> "Pseudospectral", PeriodicInterpolation -> True]["DifferentiationMatrix"]?
|
|
| May 28, 2021 at 12:46 | history | edited | xzczd♦ | CC BY-SA 4.0 |
simplify the code a bit.
|
| May 28, 2021 at 12:40 | comment | added | Gummala Navneeth | @xzczd ,@alex the reason I made dMatrixLagrange function --(myd ) is, if initial states function were approximated with some periodic functions using Sin , Cos (Fourier discrete), instead of Lagrange or Legendre functions, Then " NDSolve`FiniteDifferenceDerivative[1, tpoints, DifferenceOrder -> "Pseudospectral"]["DifferentiationMatrix"] " won't be of help isn't it?. | |
| May 28, 2021 at 12:31 | comment | added | Gummala Navneeth | @xzczd, my work is based on this lecture , youtube.com/watch?v=NkqkdxwoIgU&t=2952s | |
| May 28, 2021 at 12:28 | vote | accept | Gummala Navneeth | ||
| May 28, 2021 at 12:05 | history | edited | xzczd♦ | CC BY-SA 4.0 |
added 344 characters in body
|
| May 28, 2021 at 12:00 | comment | added | xzczd♦ | @alex Oh I forgot about Chebyshev–Gauss–Lobatto grid. Check my edit. | |
| May 28, 2021 at 11:59 | history | edited | xzczd♦ | CC BY-SA 4.0 |
added 344 characters in body
|
| May 28, 2021 at 11:50 | comment | added | Alex Trounev |
@xzczd Nice approach (+1). It looks better with npoints = 31; myd = NDSolveFiniteDifferenceDerivative[1, tpoints, DifferenceOrder -> 8]["DifferentiationMatrix"];`.
|
|
| May 28, 2021 at 11:28 | comment | added | xzczd♦ |
@Gummala The i.c. is imposed with {1.}~Join~.
|
|
| May 28, 2021 at 10:47 | comment | added | Gummala Navneeth | @ xzczd, hi ,using RootFind approach , I won't be able to give my initial condition (start points of states) .Theta1[0]==1 and Theta2[0]==1. Would you suggest me some way to do that. | |
| May 28, 2021 at 10:44 | comment | added | Gummala Navneeth | @ xzczd, link to dMatrixLagrange- " en.wikipedia.org/wiki/Lagrange_polynomial ". in the "Derivatives" section.(For the first derivative, the coefficients are given by--) | |
| May 28, 2021 at 10:22 | history | answered | xzczd♦ | CC BY-SA 4.0 |