Help with some subtleties of Runge-Kutta 4 method

[Biftheunderstudy]

I've been trying to solve a set of coupled differential equations for a while. The first 6 are 1st order ODE's in time, with no explicit time dependance. The last equation is a second order in space, and is a constraint equation.

I'm programming in Fortran 90 with a sideproject involving Matlab. My current strategy for solving the set of equations is to perform RK4 on the first 6 equations, break the last into 2 first orders ODE's and perform a separate RK4 on the now 2 equations.

I've run into a few problems. I've stored all of the independent variables in arrays with values defined at discrete grid points. Solving the constraint equation then has a bit of a problem since it relies on these variables.

Basically, in the RK4 scheme, the routine makes calls like:

K2 = h*func(x+dx/2,y+K1/2)

The problem is that my function 'func' is only defined on the grid with spacing dx, so a call to x with x+dx is asking for a value between the grid spacing.

I'm fishing for new ideas to get around this issue, any help is appreciated.

 

[Ken g6]

It took me awhile to figure this one out. If your function is only defined as points, technically it doesn't have a derivative. If an approximation of the function is acceptable, you might want to try interpolation, but that's only going to give you an approximate answer, and not necessarily a reasonable one.

This looks like it might be better asked in the Highly Technical forum.

 

[Fox5]

The problem is that my function 'func' is only defined on the grid with spacing dx, so a call to x with x+dx is asking for a value between the grid spacing.

I don't understand this.
I would think you'd have points like:
x1 x2 x3 x4
And each one would be dx space apart? Why would x+dx then be between the grid spacing?

 

[Ken g6]

Based on Wikipedia, and his earlier statement, I think he meant x+dx/2.