Name: ode-midpoint
Owner: scijs
Description: Integrate a system of ODEs using the Second Order Runge-Kutta (Midpoint) method
Created: 2015-07-24 15:49:59.0
Updated: 2015-08-01 19:15:39.0
Pushed: 2015-08-01 17:46:34.0
Homepage: null
Size: 172
Language: JavaScript
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Integrate a system of ODEs using the Second Order Runge-Kutta (Midpoint) method
This module integrates a system of ordinary differential equations of the form
is a vector of length 
. Given time step 
, the midpoint method integrates the ODE with update 
m install ode-midpoint
midpoint = require('ode-midpoint')
deriv = function(dydt, y, t) {
dt[0] = -y[1]
dt[1] = y[0]
y0 = [1,0]
n = 1000
t0 = 0
dt = 2.0 * Math.PI / n
integrator = midpoint( y0, deriv, t0, dt )
ntegrate 1000 steps:
grator.steps(n)
ntegrate all the way around a circle:
> integrator.y = [ 1.0000001939636542, 0.000041341220643982546 ]
require('ode-midpoint')( y0, deriv, t0, dt )Arguments:
y0: an array or typed array containing initial conditions. This vector is updated in-place with each integrator step.deriv: a function that calculates the derivative. Format is function( dydt, y, t ). Inputs are current state y and current time t, output is calcualted derivative dydt.t0: initial time 
.dt: time step .Returns: Initialized integrator object.
Properties:
n: dimension of y0.y: current state. Initialized as a shallow copy of input y0.deriv: function that calcualtes derivative. Initialized from input. May be changed.t: current time, incremented by dt with each time step.dt: time step . Initialized from input dt. May be changed.Methods:
.step(): takes a single step of the midpoint integrator and stores the result in-place in the y property..steps( n ): takes n steps of the midpoint integrator, storing the result in-place in the y property.(c) 2015 Ricky Reusser. MIT License