How Can I Perform a Double Integration of a Function with Given Data Sets?

[anirban84]

I need to do a double integration of the form

int{ int{ f(x(t1),y(t2)) dt1 dt2 } } limit over t1 {0 : pa} and over t2 {o:pb}.

Now i have a data set for x for equal spaced t1 values varing from 0 to pa .
and for y for equal spaced t2 values varing from 0 to pb.

I will be very happy if anyone could help me ?

 

[rcgldr]

There may be better methods but the only way I solved differential equations with software was via the Runge-Kutta method:

http://en.wikipedia.org/wiki/Runge-Kutta

The issue here is you need an initial state, for example for ballistics, you'd need the initial position and velocity. These would be used to calcuate accelerations, and the Runge Kutta method would be used to predict a new position and velocity after a very small period of time had passed. This process is repeated until the path is "completed".

For the first few steps, some type of feedback loop is needed to make the initial predictions more accurate.