Copyright	(c) Alberto Ruiz 2010
License	GPL
Maintainer	Alberto Ruiz
Stability	provisional
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.ODE
import Numeric.LinearAlgebra
import Numeric.LinearAlgebra.Util(mplot)

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)

Synopsis

Documentation

odeSolve Source

Arguments

:: (Double -> [Double] -> [Double])	x'(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 Source

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)	x'(t,x)
-> Vector Double	initial conditions
-> Vector Double	desired solution times
-> Matrix Double	solution

A version of odeSolveVWith with reasonable default step control.

odeSolveVWith Source

Arguments

:: ODEMethod
-> StepControl
-> Double	initial step size
-> (Double -> Vector Double -> Vector Double)	x'(t,x)
-> 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 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.

type Jacobian = Double -> Vector Double -> Matrix Double Source

data StepControl Source

Adaptive step-size control functions

Constructors

X Double Double	abs. and rel. tolerance for x(t)
X' Double Double	abs. and rel. tolerance for x'(t)
XX' Double Double Double Double	include both via rel. tolerance scaling factors a_x, a_x'
ScXX' Double Double Double Double (Vector Double)	scale abs. tolerance of x(t) components