Partial differential equations with mathematica

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Discussion Overview

The discussion focuses on the capabilities of Mathematica 7 in solving nonlinear second order partial differential equations (PDEs), particularly in the context of groundwater flow modeling. Participants explore syntax issues, numerical solutions, and the necessity of initial and boundary conditions.

Discussion Character

  • Technical explanation
  • Homework-related
  • Debate/contested

Main Points Raised

  • One participant inquires about the ability of Mathematica 7 to solve nonlinear second order PDEs using DSolve, noting that the output returns the original question.
  • Another participant suggests that while Mathematica can solve PDEs with known solutions, nonlinear second order PDEs typically lack such solutions, implying a need for numerical methods.
  • A suggestion is made to test a very simple example with a known closed form solution to troubleshoot the use of Mathematica before tackling the more complex problem.
  • The original poster provides a specific groundwater flow equation and expresses difficulty in obtaining a solution, questioning the need for initial and boundary conditions when using numerical methods like FEM/FDM in Mathematica.

Areas of Agreement / Disagreement

Participants express differing views on the capabilities of Mathematica 7 regarding nonlinear PDEs, with some advocating for numerical approaches while others emphasize the importance of testing simpler examples. The discussion remains unresolved regarding the specific syntax and methods for solving the groundwater flow equation.

Contextual Notes

There are limitations regarding the assumptions about the solvability of nonlinear PDEs and the dependence on specific initial and boundary conditions for numerical methods. The discussion does not clarify these aspects fully.

abbeynewton
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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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abbeyNewton said:
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.
 
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
 

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