@Adel Khaled, I would do this analytically, at least for a while. SOme of your posting was cut off on th left edge, but here's what I got:
Eqn 24 defines Re(x,t,P0,P1,P2).
Eqn 25 defines J(P0,P1,P3) as the definite integral over the x,t unit square of Re().
Eqn 26 is 3 equations invoving P0,P1,P2. The equations are in fact that the deirvatives of J with respect to P0,P1,P2 are zero. You will use to these three equations to solve for the three unknowns.
To do it, you must actualy do some algebra and basic calculus to work out the analytic equations 26a, 26b, 26c. You can do this, I think, because eqn 24, even though it is long, is really not bad and is integrable without great difficulty. You will note that Eqn 24 may be written as
Re(x,t,P0,P1,P2) = A*exp(x) + B*t*exp(x) + C*t^2*exp(x) = (A + Bt + Ct^2)*exp(x)
where A and B and C are (complicated but workable) functions of P0,P1,P2.
Use the result above to do the integral in eqn 25. Then you will have J=f(P0,P1,P2).
Then I would compute the derivatives of J with respect to P0, P1, P2, analytically. Use fsolve() t find the values of P0, P1, P2 tht make all three equations equal to zero.
