Using runge kutta for solving system of nonlinear first order ODEs

Question

I'm completely stuck with one of my problem sets.

I'm supposed to solve the following system of ODEs using Matlab:

o'(u) = R-acos(u)/sqrt(b^2 + (R-acosu)^2)
e'(u) = Rcos(o)
n'(u) = Rsin(o)
R,a,b are constants
u goes from 0 to 2pi

I'm supposed to use the Runge Kutta method, which I haven't tried before. I've been at it for quite some time but don't even know where to start - which is why I don't really have any code to show you. I have been doing a lot of googleing but without results.

If anyone could give me a hand it would be much appreciated!

Lutz Lehmann Lutz Lehmann · Accepted Answer · 2015-05-06T09:14:34

Read the friendly manual available at mathworks on the use of ODE solvers and the syntax of calling a specific solver. The classical way here would be

function yprime = odefunc(u,y,R,a,b)
    o=y(1); e=y(2); n=y(3);
    oprime = R-a*cos(u)/sqrt(b^2 + (R-a*cos(u))^2);
    eprime = R*cos(o);
    nprime = R*sin(o);
    yprime = [oprime; eprime; nprime ];
end //function

and after defining initial conditions, time frames and parameters, call it as

[t,y] = ode45(@(t,y) odefunc(t,y,R,a,b), [t0, tf], [o0; e0; n0])

Using runge kutta for solving system of nonlinear first order ODEs

1 Answers