<runge-kutta> ( initial-delta dxn..n/dt initial-x..nt t-limit -- seq )

Vocabulary

math.runge-kutta

Inputs

initial-delta	a number
dxn..n/dt	a sequence
initial-x..nt	a sequence
t-limit	a number

Outputs

seq	a sequence

Word description

Simple runge-kutta implementation for generating approximated solutions for a set of first order differential equations

Examples

A lorenz attractor is a popular system to model with this:

USING: math.runge-kutta math.runge-kutta.examples ; lorenz.

note that the produced chart is a 2 dimensional representation of a 3 dimensional solution. Similarly, the rabinovich-fabrikant system (stable alpha-gamma limit cycle):

USING: math.runge-kutta math.runge-kutta.examples ; rabinovich-fabrikant.

Definition

USING: kernel sequences ;

IN: math.runge-kutta

: <runge-kutta>
    ( initial-delta dxn..n/dt initial-x..nt t-limit -- seq )
    time-limit-predicate
    [ [ runge-kutta ] [ 2drop f ] if ] compose with follow nip ;