hmatrix-0.11.0.0: Linear algebra and numerical computation

Portability uses ffi provisional Alberto Ruiz (aruiz at um dot es)

Numeric.GSL.ODE

Description

Solution of ordinary differential equation (ODE) initial value problems.

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)

sol = odeSolve xdot [10,0] ts

main = mplot (ts : toColumns sol)```

Synopsis

# 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) -> Maybe (Double -> Vector Double -> Matrix Double) optional jacobian -> Vector Double initial conditions -> Vector Double desired solution times -> Matrix Double solution

Evolution of the system with adaptive step-size control.

data ODEMethod Source

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 `RKf45`. 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 Implicit 2nd order Runge-Kutta at Gaussian points. RK4imp Implicit 4th order Runge-Kutta at Gaussian points. BSimp Implicit Bulirsch-Stoer method of Bader and Deuflhard. This algorithm requires the Jacobian. Gear1 M=1 implicit Gear method. Gear2 M=2 implicit Gear method.

Instances

 Bounded ODEMethod Enum ODEMethod Eq ODEMethod Show ODEMethod