ode-rk4
v1.1.3
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Integrate a system of ODEs using the Fourth Order Runge-Kutta (RK-4) method
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ode-rk4
Integrate a system of ODEs using the Fourth Order Runge-Kutta (RK-4) method
Introduction
This module integrates a system of ordinary differential equations of the form
where is a vector of length . Given time step , the Runge-Kutta 4 method integrates the ODE with update
For a similar adaptive method using the fifth order Cash-Karp Runge-Kutta method with fourth order embedded error estimator, see [https://github.com/scijs/ode45-cash-karp](ode45-cash-karp].
Install
$ npm install ode-rk4
Example
var rk4 = require('ode-rk4')
var deriv = function(dydt, y, t) {
dydt[0] = -y[1]
dydt[1] = y[0]
}
var y0 = [1,0]
var n = 1000
var t0 = 0
var dt = 2.0 * Math.PI / n
var integrator = rk4( y0, deriv, t0, dt )
// Integrate 1000 steps:
integrator.steps(n)
// Integrate all the way around a circle:
// => integrator.y = [ 0.9999999999995743, -8.160481752145232e-11 ]
API
require('ode-rk4')( 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 isfunction( dydt, y, t )
. Inputs are current statey
and current timet
, output is the calculated derivativedydt
.t0
: initial time .dt
: time step .
Returns: Initialized integrator object.
Properties:
n
: dimension ofy0
.y
: current state. Initialized as a shallow copy of inputy0
.deriv
: function that calculates the derivative. Initialized from input. May be changed.t
: current time, incremented bydt
with each time step.dt
: time step . Initialized from inputdt
. May be changed.
Methods:
.step()
: takes a single step of the RK-4 integrator and stores the result in-place in they
property..steps( n )
: takesn
steps of the RK-4 integrator, storing the result in-place in they
property.
Credits
(c) 2015 Ricky Reusser. MIT License