| Copyright | (c) Alberto Ruiz 2010 |
|---|---|
| License | GPL |
| Maintainer | Alberto Ruiz (aruiz at um dot es) |
| Stability | provisional |
| Portability | uses ffi |
| Safe Haskell | None |
| Language | Haskell98 |
Numeric.GSL.ODE
Description
Solution of ordinary differential equation (ODE) initial value problems.
http://www.gnu.org/software/gsl/manual/html_node/Ordinary-Differential-Equations.html
A simple example:
@import Numeric.GSL import Numeric.LinearAlgebra import Graphics.Plot
xdot t [x,v] = [v, -0.95*x - 0.1*v]
ts = linspace 100 (0,20 :: Double)
sol = odeSolve xdot [10,0] ts
main = mplot (ts : toColumns sol)@
- odeSolve :: (Double -> [Double] -> [Double]) -> [Double] -> Vector Double -> Matrix Double
- odeSolveV :: ODEMethod -> Double -> Double -> Double -> (Double -> Vector Double -> Vector Double) -> Vector Double -> Vector Double -> Matrix Double
- data ODEMethod
- type Jacobian = Double -> Vector Double -> Matrix Double
Documentation
Arguments
| :: (Double -> [Double] -> [Double]) | xdot(t,x) |
| -> [Double] | initial conditions |
| -> Vector Double | desired solution times |
| -> Matrix Double | solution |
A version of odeSolveV with reasonable default parameters and system of equations defined using lists.
Arguments
| :: ODEMethod | |
| -> Double | initial step size |
| -> Double | absolute tolerance for the state vector |
| -> Double | relative tolerance for the state vector |
| -> (Double -> Vector Double -> Vector Double) | xdot(t,x) |
| -> Vector Double | initial conditions |
| -> Vector Double | desired solution times |
| -> Matrix Double | solution |
Evolution of the system with adaptive step-size control.
Stepping functions
Constructors
| RK2 | Embedded Runge-Kutta (2, 3) method. |
| RK4 | 4th order (classical) Runge-Kutta. The error estimate is obtained by halving the step-size. For more efficient estimate of the error, use the embedded methods. |
| RKf45 | Embedded Runge-Kutta-Fehlberg (4, 5) method. This method is a good general-purpose integrator. |
| RKck | Embedded Runge-Kutta Cash-Karp (4, 5) method. |
| RK8pd | Embedded Runge-Kutta Prince-Dormand (8,9) method. |
| RK2imp Jacobian | Implicit 2nd order Runge-Kutta at Gaussian points. |
| RK4imp Jacobian | Implicit 4th order Runge-Kutta at Gaussian points. |
| BSimp Jacobian | Implicit Bulirsch-Stoer method of Bader and Deuflhard. The method is generally suitable for stiff problems. |
| RK1imp Jacobian | Implicit Gaussian first order Runge-Kutta. Also known as implicit Euler or backward Euler method. Error estimation is carried out by the step doubling method. |
| MSAdams | A variable-coefficient linear multistep Adams method in Nordsieck form. This stepper uses explicit Adams-Bashforth (predictor) and implicit Adams-Moulton (corrector) methods in P(EC)^m functional iteration mode. Method order varies dynamically between 1 and 12. |
| MSBDF Jacobian | A variable-coefficient linear multistep backward differentiation formula (BDF) method in Nordsieck form. This stepper uses the explicit BDF formula as predictor and implicit BDF formula as corrector. A modified Newton iteration method is used to solve the system of non-linear equations. Method order varies dynamically between 1 and 5. The method is generally suitable for stiff problems. |