# convergence criteria

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 October 9, 2002, 04:50 convergence criteria #1 student Guest   Posts: n/a 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

 October 9, 2002, 20:09 Re: convergence criteria #2 Wei Guest   Posts: n/a 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

 October 10, 2002, 02:58 Re: convergence criteria #3 student Guest   Posts: n/a 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

 October 12, 2002, 02:35 Re: convergence criteria #4 S. S. Mudthir Guest   Posts: n/a which one of Anderson books?

 October 13, 2002, 06:50 Re: convergence criteria #5 student Guest   Posts: n/a Intorduction to cfd book by anderson

 October 14, 2002, 03:51 Re: convergence criteria #6 student Guest   Posts: n/a sorry computational fluid dynamics basics and applications by John D anderson

 October 15, 2002, 01:44 Re: convergence criteria #7 S. S. Mudthir Guest   Posts: n/a 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.