# RK4integrator

implements the classical Runge-Kutta scheme (aka RK4).

## Contents

- Syntax
- Description
- Input Arguments
- Output Arguments
- See Also
- References

## Syntax

xNext = RK4integrator(x,u,w,funHandle,dt)

## Description

This function implements the classical Runge-Kutta scheme and, in addition to solving the initial value problem x_dot = f(x,u,w), x(0) = x0 numerically, can be used for time-discretizing continuous-time dynamical systems, e.g. for reachability analysis using CORA. Both the control input "u" and the disturbance "w" are assumed to be constant during the time step.

## Input Arguments

x0 | initial state (real array of dimension [nx,1])
u | control input (real array of dimension [nu,1])
w | disturbance (real array of dimension [nw,1])
funHandle | function handle to the dynamics function of the continuous-time system (x_dot = f(x,u,w);
dt | time step (positive scalar)

## Output Arguments

xNext | state at the end of the time interval [0, dt] (real array of dimension [nx,1])

## See Also

-

## References

[1] W. Kutta, "Beitrag zur näherungsweisen Integration totaler Differentialgleichungen", Zeitschrift für Mathematik und Physik, 46: 435–453, 1901.

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