you can use "Minitab" software. 

In which such facility is available

hi

A suggestion: 1 Fit a multinomial to data as Y = a0 x1+ a1 x1^2.. + b0 x2 + b1 x2^2  ...

                       2 we can get system of PDE .

                          partialY/partial x= a0 + 2a1 x1 ...

                          partialY/partialz = b0 + 2b1 x2...

                   ie   vector equation x vector [ x1 x2 ..]

                       partial Y/ .partial x   = [A ] [f(x1) , f(x1) ...}Transp

                         3 invert A to get  fx(1) = A^-1 [ partial Y/ .partial x ]

                   hope it helps..

Cheers

Ibrahim, You probably should specify the problem more exactly.

If you are doing simple econometrics and estimate the regression on 3 independent variables, like W(x,y,z)=a+bx+cy+dz+eps, I do not see the room for differential equation.

If you study time dependent process with time lags, then you can get corresponding difference equation, and then can find analog in differential equation.

Finally, if you want to check if your data set fits some known differential equation having some parameters, you have to solve it analytically, and estimate the difference between the data set and your solution minimizing the sum of squares of differences.

The variables dependent on each other instead of time we can see the room for differential equation. let say Parameter A depends on B, C and D. but I want to formulate an equation between A and any of other parameters say dA/dB=?'something here', the equation should link all the parameters. Is it possible to do this using data from an experiment.  

I'm lost, first you wrote that you have "three independent variables and one dependent". But in last post you wrote "The variables dependent on each other". It's difficult to understand the problem...

If you mean you want to fit a $M$-dimensional vector-valued system parameter $p$ in an $N$-dimensional ode system $y'(t) = f(t,y;p)$ so that its numerical solution $y(t_i)$ at different time issues $t_i$, $i=1,\ldots,M$ fits associated measurements $\tilde y_i$, $i=1,\ldots,M$, for example in a least squares sence, you can do this by an appropriate drect multiple shooting method; see the literature of Georg Bock, University of Heidelberg, Germany, who was the first who developed a code for such an inverse problem. To my knowledge his codes are still among the most powerful ones.

Perhaps an almost universal solution is to use stochastic optimization. If you are interested, you can see what I did in my paper Person-by-person prediction of intuitive economic choice. It can be found as full text in my profile here in ResearchGate. Good luck!

You may use ndCurveMaster to data fit of an unlimited number of input variables

But If you send me data in a CSV file to [email protected], I will quickly develop some regression equations for you.

Tomasz Cepowski

You can use LS Optimizer Software:

http://zeus.df.ufcg.edu.br/labfit/LS.htm.

This is not so easy as curve fitting for a function. You need build a solver.exe for the differential equation (direct problem). Then, LS executes your solver to determine the sensitivities of the parameters using Levenberg-Marquardt algorithm.