| Author | Message | ||
     Raimund Gottkehaskamp (gottkehaskamp) New member Username: gottkehaskamp Post Number: 2 Registered: 06-2004 |
Since Version 3 there is a new second order sheme for time integration algorithms implemented. Can anyone give me a hint, where I can find more detaild information about this sheme? | ||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 315 Registered: 06-2003 |
The method used in FlexPDE is a second-order Backward Difference Formula (BDF), widely discussed as "Gear's Method" after its initial introduction by Gear in 1971. The principle is that one fits a polynomial to a number of time values, all of which are known except the last. This provides an implicit equation for the last value in the time sequence. The first-order member of this family (which you can request in FlexPDE version 4 by "SELECT torder=1") is simply the venerable Backward Euler method, selected in FlexPDE version 3 by "SELECT TCENTER=1". One reference I have used is "Numerical Solution of Initial-Value Problems and Differential-Algebraic Equations" by Brenan, Campbell and Petzold, SIAM, 1996. |