# Partial differential equations with mathematica

• Mathematica

## Main Question or Discussion Point

hello, i just want to ask if mathematica 7 can solve nonlinear second order partial differential equations. i tried solving it with DSolve but it kept on giving me the question back as the output....please is there any way or syntax for solving it on mathematica 7?...thanks for any suggestions.

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Dale
Mentor
hello, i just want to ask if mathematica 7 can solve nonlinear second order partial differential equations. i tried solving it with DSolve but it kept on giving me the question back as the output....please is there any way or syntax for solving it on mathematica 7?...thanks for any suggestions.
Mathematica can solve any PDE for which a solution is known. However, there are going to be very few, if any, known solutions for nonlinear 2nd order PDE's. You will probably need to do it numerically.

Pick a VERY simple example where you know there is a closed form solution and that you can do by hand. Then try it with Mathematica and see if you can get it to do it. If you cannot then post the example and how you tried to do it. Once you have seen how to do a very simple example work that should eliminate all kinds of errors and misunderstandings and you can look at the actual problem you have.

Dale
Mentor
Excellent suggestion!

ok...the equation is a groundwater flow equation...which is

T*(d squared h/dx squared +d squared h/dy squared) +N=S*dh/dt....where s is storativity N is recharge and T is Transmissivity. i tried entering this and it returned it as output...actually this can be solved using FEM/FDM but how can i do that using mathematica...is there any need to put the initial/boundary conditions??...need answers as am working on a final year project involving groundwater modelling....thanks