Numeric.GSL.ODE

hmatrix-0.9.3.0: Linear algebra and numerical computation

Numeric.GSL.ODE

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

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)

sol = odeSolve xdot [10,0] ts

main = mplot (ts : toColumns sol)

Synopsis

odeSolve :: (Double -> [Double] -> [Double]) -> [Double] -> Vector Double -> Matrix Double

odeSolveV :: ODEMethod -> Double -> Double -> Double -> (Double -> Vector Double -> Vector Double) -> Maybe (Double -> Vector Double -> Matrix Double) -> Vector Double -> Vector Double -> Matrix Double

data ODEMethod

= RK2

| RK4

| RKf45

| RKck

| RK8pd

| RK2imp

| RK4imp

| BSimp

| Gear1

| Gear2

Documentation

odeSolve

Source

:: 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

Source

:: 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

Produced by Haddock version 2.6.1