Re: boundary condition for NDSolve
- To: mathgroup at smc.vnet.net
- Subject: [mg45081] Re: [mg45036] boundary condition for NDSolve
- From: CAP F <Ferdinand.Cap at eunet.at>
- Date: Tue, 16 Dec 2003 06:21:07 -0500 (EST)
- References: <200312150926.hBF9QV5b005329@jupiter.kanazawa-it.ac.jp>
- Sender: owner-wri-mathgroup at wolfram.com
Yama Masu wrote: > > Hi, Ferdinand. > > Thanks for quick and useful response. Let me ask you something more. > > > 2.)Your membrane pde is of elliptic type. Then theory says that for > > elliptic pde ONLY ONE boundary can be given except you place a > > singularity within the center of the inner boundary domain. > > Well, could you tell me the more detail. Physically, it is possible to > make a membrane between two squares and it is also possible to have it > vibrate. The boundary condition can be more than two. Hi, Masu The problem is that NDSolve cannot solve problems with 2 different boundary conditions for an elliptic pde. Sure, it is however possible to solve such problems using other numerical methods, like boundary element method, finite element method, collocation methods. > >3.)Your problem has been solved and published, see below: > >page 263, chapter 5.2, "Boundary problems with two closed boundaries" > > Thank you. I read this. But this sample does not use NDSolve. You are correct. My example did not use NDSolve. Since I told you that NDSolve cannot work for 2 boundaries, I just wanted to give you an example how to use collocation methods to solve such problems. More details are in my book > >1.)NDSolve is not well suited to solve part de. It can do this for > >very few pde. > > Combined with 3), can I understand that it is impossible to impose > two boundary condition in NDSolve? Yes, you may assume that it is impossible to impose two boundary conditions in NDSolve !! To solve the problem you may use either : 1)numerical integration using finite differences or finite elements or collocation methods 2) assume a closed expression with many unknown parameters and include a singularity in the center of the inner domain. Since Cartesian solution of the membrane equation has singularities only in the infinity point, it may be usefull to solve the problem in polar coordinates and write up a Bessel function solution, see the example in codes 44,45,46, and 47. Due to the Bessel function Y one then has a singularity at the origin and one may use outer collocation methods. Your problem is interesting and I will try to have time and solve it. May be you hear from me within several days. Greetings to your wonderful country (I have been there as Guestprofessor in Sendai, Kyoto and congress in Tokyo.) Regards. > Yama Masu