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 student October 9, 2002 04:50

convergence criteria

hi I want to know whether it is possible to find the convergence criteria for expicit method in finite difference. for all types of partial differential equations. like first order and second degree. if yes how can we bye

 Wei October 9, 2002 20:09

Re: convergence criteria

This must be the first thing to do before using any explicit method in finite difference scheme. Von Neumann analysis is usually used to find the convergence criteria. This method simply use complex Fourier series to approximate the round-off error. Although it is derived for linear system, it also supply necessary stable condition for nonlinear equations. Different system may end up with different criteria. You can find the analysis in many CFD textbook, for example, "computational fluid mechanics and heat transfer" by John C. Tannehill, Dale a. Anderson and Richard H. Pletcher.

Hope it help Wei

 student October 10, 2002 02:58

Re: convergence criteria

Hi Could you do it for a simple equation given below like delu/delt=A-SQRT(1+(delu/delx)**2) since I was not able to do it as it was givenm in anderson book. for explicit finite difference scheme please help

 S. S. Mudthir October 12, 2002 02:35

Re: convergence criteria

which one of Anderson books?

 student October 13, 2002 06:50

Re: convergence criteria

Intorduction to cfd book by anderson

 student October 14, 2002 03:51

Re: convergence criteria

sorry computational fluid dynamics basics and applications by John D anderson

 S. S. Mudthir October 15, 2002 01:44

Re: convergence criteria

Hi, I started this book many days ago and still progressing, I reached the fifth Chapter and till now I didn't find such a problem. May be it is sill in the coming chapters, If you like when can have some discussion with it very soon.

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