M371 - Alexiades
Review4a: for FINAL - ODEs
Material
ODE integrators (numerical solution of ODEs)
Concepts for ODEs
well posed problem: solution exists, is unique, depends continuously on data
Types of ODE solvers: explicit/implicit; single-step/multi-step; predictor-corrector; adaptive; symplectic
Families of ODE solvers: Runge-Kutta, multistep (Adams-Bashforth, Adams-Moulton), BDF for stiff, ... many others...
Methods for ODEs
Euler method for IVPs, basic idea for other methods
For each Method should know: what it is for, idea, advantages/disadvantages, and:
| Method |
know |
order |
explicit/implicit |
single/multi-step |
| Euler (forward) | algo |
1st |
explicit |
single step |
| backward Euler | algo |
1st |
implicit |
single step |
| classical RK | idea |
4th |
explicit |
single step |
| RKF45 | idea |
4th |
explicit |
single step, adaptive |
| Adams-Bashforth | − |
high |
explicit |
multistep |
| Adams-Moulton | − |
high |
implicit |
multistep |
| Gear BDF | − |
high |
implicit |
multistep, for stiff |