2nd order ODE using Runge-Kutta method in C

Question

I want to model the motion of a particle using a set of 2nd order equations the the equation is

d2x/dt2 = 1 + dy/dt + dz/dt 
d2y/dt2 = 1 + dx/dt + dz/dt 
d2z/dt2 = 1 + dx/dt + dy/dt

vector V is (dx/dt dy/dt dz/dt), X is (x y z), V = [0 0 0], X = [0 0 0] initially

I implemented this into C code for one of the ODEs below CODE;

double X_function(double a[], double t, double at[],double b[],double c[]) {
//double yt, zt;
at[0] = a[0];
at[1] = 1 + b[0] + c[0];
double F = at[1];
return F;
}

i need help understanding how to use R-K in such a case

We are not a coding service. This looks like a mathematical problem anyway, not a programming problem. So, how is this specific to the C programming language? — too honest for this site, May 27 '17 at 14:08
The code has to be written in C and I just need help in understanding how R-K metod works for second order ODEs — Gabriel Richard, May 27 '17 at 14:11
As I wrote: That's a pure math problem, not programming. What have you done to find out yourself? How about a good math book? — too honest for this site, May 27 '17 at 14:12
Perhaps [Mathematics Stack Exchange](https://math.stackexchange.com/search?q=Runge-Kutta) is the place to go, and/or some googling. — Weather Vane, May 27 '17 at 14:13

score 1 · Answer 1 · answered May 27 '17 at 15:33

1

You have an equation

x''=F(x,x')

that you rewrite as an first order system

x' = v
v' = F(x,v)

Implement this coupled 6-dimensional system as one function

void derivs(double u[], double t, double du[]) {
    int j,k;
    for(k=0; k<3; k++) {
        du[k] = u[3+k];
        du[3+k] = 1;
        for(j=0;j<3; j++) 
            if(j!=k) du[3+k] += u[j]
    }
}

then you can implement the Runge-Kutta method in a general form for a first-order system.

answered May 27 '17 at 15:33

Lutz Lehmann

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Just to understand it better how can i get an output from this function? – Gabriel Richard May 28 '17 at 17:59
The output is in `du`. As you pass only the pointer, the array you pass in the call to the `derivs` function will still contain the new values after the call. – Lutz Lehmann May 28 '17 at 20:12

2nd order ODE using Runge-Kutta method in C

1 Answers1