| Author | Message | ||
     Fernando Buezas (fernandob) New member Username: fernandob Post Number: 2 Registered: 02-2007 |
Dear Nelson: I understand than the temporal integrator this based in the finite-difference Gear method of second order. Exists any other way to use another integrator like for example Runge Kuta? | ||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 773 Registered: 06-2003 |
No. Runge-Kutta is an explicit method. The multi-step Backward Difference Formula method (Gear's method) used in FlexPDE is fully implicit, and is specifically designed to handle stiff systems. Strictly speaking, it is not a finite-difference method, as it uses an interpolation function and differentiates the interpolator to determine the time derivative at the end of the multi-step interval. In this sense, it is similar in spirit to the finite element method, and makes a smooth match with finite elements in space. You can select the order of interpolation with SELECT TORDER=number. FlexPDE supports orders 1,2 or 3. TORDER=1 is the backward Euler method. According to Stefan Jahn at http://qucs.sourceforge.net/tech/node27.html: "There is no more stable second order integration method than the Gear's method of second order. Only implicit Gear methods with order <=6 are zero stable." According to Ascher and Petzold ("Computer Methods for Ordinary Differential Equations and Differential Algebraic Equations", 1998), multi-step backward difference formulas are currently the most popular methods for solving stiff systems. | ||
| Fernando Buezas (fernandob) Junior Member Username: fernandob Post Number: 3 Registered: 02-2007 |
Many thanks Mr. Nelson. Your answer has served much to me. Thanks for this product. It is spectacular! |