Runge-Kutta matlab library

Question

JC 2022-4-22

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https://ww2.mathworks.cn/matlabcentral/answers/1702410-runge-kutta-matlab-library

编辑： James Tursa 2022-5-3

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)

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Walter Roberson 2022-4-22

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 2022-4-23