ode-midpoint

    1.0.6 • Public • Published

    ode-midpoint Build Status npm version Dependency Status

    Integrate a system of ODEs using the Second Order Runge-Kutta (Midpoint) method

    Introduction

    This module integrates a system of ordinary differential equations of the form

    undefined

    undefined

    where undefined is a vector of length undefined. Given time step undefined, the midpoint method integrates the ODE with update

    undefined

    Install

    $ npm install ode-midpoint

    Example

    var midpoint = require('ode-midpoint')
     
    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 = midpoint( y0, deriv, t0, dt )
     
    // Integrate 1000 steps:
    integrator.steps(n)
     
    // Integrate all the way around a circle:
    // => integrator.y = [ 1.0000001939636542, 0.000041341220643982546 ]

    API

    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 undefined.
    • dt: time step undefined.

    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 undefined. 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.

    Credits

    (c) 2015 Ricky Reusser. MIT License

    Install

    npm i ode-midpoint

    DownloadsWeekly Downloads

    1

    Version

    1.0.6

    License

    MIT

    Last publish

    Collaborators

    • jaspervdg
    • mikolalysenko
    • planeshifter
    • rreusser