Function returning incorrect value

[teplotaxl]

Hi all!

I'm trying to model a differential equation having to do with free fall, using RK4 and Fortran 90. The equation is:

[tex]\ddots{y}(t)=-g \frac{R^2}{y^2}[/tex]

The code is attached in caidalibre.f90

The big problem is that function f(y,v,t) returns an unexpected value within the main program. Moreover, the program yields results which would indicate the object is ascending, and not descending. Any insight will be greatly appreciated.

Cheers!

PS: I am using

gfortran
Using built-in specs.
Target: powerpc-apple-darwin8.9.0
Configured with: ../gcc-4.3-20070810/configure --enable-threads=posix --enable-languages=fortran
Thread model: posix
gcc version 4.3.0 20070810 (experimental)

 

[mikrom]

Simply proove if you don't have an error in the Runge-Kutta formula you use.

But the strange behaviour can be caused by the nature of numerical treatment of differential equations:
In most cases you need to use the step control algorithm, which automatically decreases the integration step on critical intervals or increases it where it's possible.
The other special class are so called stiff differential equations. These equations cannot be integrated either with explicit RK methods like you use here, nor using step control helps. Here you need to use implicit Runge-Kutta Methods, like backward Euler method or from higher order Radau methods,..etc. ...and naturally all with the step control.

But this thema is off topic in this forum