hmatrix-0.15.2.1: Linear algebra and numerical computation

Copyright(c) Alberto Ruiz 2010
LicenseGPL
MaintainerAlberto Ruiz (aruiz at um dot es)
Stabilityprovisional
Portabilityuses ffi
Safe HaskellNone
LanguageHaskell98

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)@

Synopsis

Documentation

odeSolve Source

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 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)

xdot(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.