hmatrix-gsl-0.19.0.1: Numerical computation

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 Graphics.Plot(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

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.

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.

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.

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