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## Runge Kutta 8th Order Integration

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Runge-Kutta 8th order numerical integration method

Updated 19 Apr 2019

In numerical analysis, the Runge–Kutta methods are a family of implicit and explicit iterative methods, which include the well-known routine called the Euler Method, used in temporal discretization for the approximate solutions of ordinary differential equations. These methods were developed around 1900 by the German mathematicians Carl Runge and Martin Kutta. Here, integration of the normalized two-body problem from t0 = 0 [s] to t = 3600 [s] for an eccentricity of e = 0.1 is implemented and compared with analytical method.

Reference:
Goddard Trajectory Determination System (GTDS): Mathematical Theory, Goddard Space Flight Center, 1989.

### Cite As

Meysam Mahooti (2021). Runge Kutta 8th Order Integration (https://www.mathworks.com/matlabcentral/fileexchange/55431-runge-kutta-8th-order-integration), MATLAB Central File Exchange. Retrieved .

Juan José Negrete

Dear Meysam.

I'm afraid that the screenshot that you posted contains a mistake. In the reference that you provided (https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19760017203.pdf) page 288, the first sum in index seven is -231, whereas you screenshot shows -234

Vasco Grilo

Tobiasz Bajek

Tobiasz Bajek

Meysam Mahooti

Dear Maksim,
The formula is taken from the following link:
Long A. C., Cappellari J. O., Velez C. E., Fuchs A. J.; Mathematical Theory of the Goddard Trajectory Determination System; Goddard Space Flight Center; FDD/552-89/001; Greenbelt, Maryland (1989).

Maksim

How it can be true if the minimum number of stages s required for an explicit s-stage Runge–Kutta method to have order 8 is 11? There is also the result obtained by Butcher (1985) that "For p≥8 no explicit Runge-Kutta method exists of order p with s = p+2 stages"

https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods
Hairer, 2008, 2nd edition, p. 179

Michael Sampol

Demi Moore

peter anderson

Sam Davidson

##### MATLAB Release Compatibility
Created with R2019a
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