ode-midpoint   

> 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

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

Install

``bash
$ npm install ode-midpoint
`

Example

`javascript
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

$3


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.

Credits

(c) 2015 Ricky Reusser. MIT License