Numeric.GSL.ODE

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)

sol = odeSolve xdot [10,0] ts

main = mplot (ts : toColumns sol)

Documentation

odeSolve

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.

odeSolveV

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

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