Without knowing the background details, I can only mention that in Mathematica one can use "Interpolation", "FunctionInterpolation", "ListInterpolation", "InterpolatingFunction", "Fit", "FindFit", etc. In general, when in need of something in Mathematica, goto: Help --> Documentation Center, or Help --> Function Navigator, or Help --> Virtual Book.

Can you be more explicit in what you are trying to do. At first glance it appears you have some equation. Is it algebraic, transcendental or differential ?. Let's suppose it ia nonlinear transcendental equation of the form F[x,y; a,b,c]=0 where x and y are the independent and dependent variables and a, b,c are the parameters. Now given a set of experimental data of ordered pairs {x_i,y_i}, you can use a nonlinear regression method to find the best fit parameters a,b,c. This can be done in Matlab and Mathematica. As Behnam pointed out you can use FindFit. MatLab has equivalent routines. Once you got the parameters your next task is to find y=G[x; a,b,c]. Well if you are dealing with a nonlinear function so that G[x; a,b,c] is not known, your best bet is to use Mathematica's ContourPlot and display the zero level set curve F[x,y; a,b,c]=0. Of course you may have multiple solutions ( i.e., for a given x you may have multiple y values that satisfy F[x,y; a,b,c]=0). From the contour plot you can get initial guesses for the y values and then use FindRoot to get a numerical y value for a given x value. If the function F[x,y; a,b,c] is a polynomial in x then you can always get numerical solution using NSolve. Note since the parameters a,b,c are not exact integers, you cannot use Mathematica to find a analytical solution to F(x,y;a,b,c) =0.

Hello

Thanks for your help

Yes but my problem is differential equation and I m not sure of it's solution form. because its general solution don't fit with experimental data.So I can lie in chance to find right solution. my experimental fit with general equation lead me to insert some nonlinearity in solution. this result in best fit but with this nonlinear assumption there is no general solution. so I have to solve it numerically and I don't have correct number. correct number are getting from solution fitting.

can 99% fitting with solution prove my guess about solution?

Thanks in advance

If you have a differential equation the task is a bit more complicated but can be readily done in Mathematica. Take a look at my publication "Estimation of Rheological Data from Polymer Melt Flow in a Circular Tube". In this example the rheological model parameters must be found by solving a nonlinear ODE for the velocity field. The Mathematica code is given in the publication. Look at the section "Estimating Carreau Parameters from Velocity Data". Hopefully this will help you figure out your problem.

Thanks in advance Dr Higgins

I'll try it and back for showing results