Runge-Kutta matlab library

Hi everybody, I am currently trying to understand this code that I have taken from this research paper: https://waterloouav.files.wordpress.com/2010/01/parachute.pdf

I have 2 questions:

1) I am trying to figure out if RK4_TI is a matlab library or did he manually write his own runge katta code as i couldnt find it in his research paper.

2) i realised he didnt assign the value of T*step to a variable, but i am unsure on what i should assign it to instead.

Hope somebody can give me some advice on this! Thank you.

clear;
T = 0.01;
end_time = 10;
num_of_steps = floor(end_time / T);

u=cell(1,num_of_steps);
x=cell(1,num_of_steps);

x{1} = [0; 0; 0; 0; 0; 0; 7; 0; 2; 0; 0; 0];

for count = 1:num_of_steps
u{count} = zeros(2,1);
end
disp = 0;
for step = 1:num_of_steps
    x{step+1}=RK4_TI(@six_dof_parachute,T,x{step},u{step});
    if disp == 100
        disp = 0;
        T*step
    else
        disp = disp + 1;
    end
end
six_dof_plot(x,u,num_of_steps,T)

[Walter Roberson]

RK4_TI is not provided by Mathworks.

T*step should not be assigned to a variable: it is intended to be displayed. It is a progress report that is displayed every 100 steps.

[JC]

Dear Walter, thank you for your help!

I see, no wonder i couldnt find anything regarding RK4_TI from Matlab's documentation. Perhaps I could use some RK4 files available in matlab file exchange to go about this problem. Cheers!

Best,

Jc

[Walter Roberson]

The only other reference to RK4_TI that I can seem to find is https://people.math.sc.edu/Burkardt/f_src/stochastic_rk/stochastic_rk.html in the context of Stochastic Differential Equations . However, the paper you are looking at does not appear to be using Stochastic Differential Equations.

[JC]

Thank you for searching for other references to RK4_TI, but you are right. I should be looking in the context of using ODEs instead.

JC

Answer 1

[Benjamin Thompson]

ode45 is the closest Runge Kutta implementation for what you are describing. Type "doc ode45" for details.

[JC]

Thank you for the suggestion! I'll look it up to see if it would be implementable or not. Cheers!

JC