Of course there are mathematical models for this problem. Otherwise, solar eclipses and their visibility conditions could neither have been computed nor predicted :)

These models are, however, relatively involved, as far as I understand. You need to model the relative positions of sun, earth and moon rather precisely, I guess. Thus, not only the orbital parameters of the various elliptical movements of these three bodies have to be taken into account, but also the forces of the other planets that change these orbits permanently. I am not sure whether one also has to take general relativity corrections into account. Probably the effect of the mass distribution in moon and earth leads to larger corrections as well. Also beware that even in the Newtonian three-body problem the orbits are not truly elliptical, even for spherical bodies. There is no closed-form solution to this Newtonian three-body problem, as far as I know. Thus, even in such a simplified model one has to use numerical methods in order to obtain the answers you are looking for.

thanks for advice......I am doing a mathematical model for this......but I am not getting the result but when I take my model in case of artificial satellite then it is giving proper result........................hopeful I will get some more fruitful response related with my question......

Here you have a source code to start with:

http://www.mathworks.es/matlabcentral/fileexchange/39358-a-matlab-script-for-predicting-solar-eclipses

thank for providing link but this link i already know, this code provides local prediction (means give lattitude, longitude of a particular place, then it will tell whether that at place solar eclipse will happen or not), not global prediction which I want........................I appreciate your information, but if you know how to predict globally, I will be more happy.............

It's a three body problem when only the sun, the earth, and the moon are considered. Three body problem is chaotic, having the well-known "butterfly effect" (sensitive dependence on initial conditions). The trajectories of the bodies change completely even if there is a small difference in the initial condition. Yet we may calculate a short term estimation. Unfortunately, long term prediction is indeed impossible.

Its possible......but how to make it....that's the biggest search...............

In fact, they are predicted with the help of a mathematical model. One of the best one was proposed by Jean and Michelle Chapront some years ago...

http://www.amazon.com/Michelle-Chapront-Touz%C3%A9/e/B001KCIJBE

thanks for information..........do you have a soft copy of the linked "Lunar Tables and Programs from 4000 B.C. to A.D. 8000", if yes please provide me @ [email protected]

Solved this problem...