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Old   July 27, 1999, 08:46
Yogesh Talekar
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Can anybody tell me where can i get some ONLINE papers or Literature for Implicit Finite Difference Methods?
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Old   July 27, 1999, 14:25
Default ONLINE: Numerical Recipes
Patrick Godon
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Hi There,

Try the book Numerical Recipes. There should there everything you wanted to know about .. what you wanted to know and what you did not want.

The book is available for free online (but the softwares they have are not):


Good Luck!

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Old   July 27, 1999, 14:41
Default ONLINE: Numerical Recipes - try this link
Patrick Godon
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You might want to try this link rather than the previous one:

here ( or there ( .

The previous link seems to have some problems.

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Old   July 28, 1999, 09:54
Default More details
Patrick Godon
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Hi Yogesh,

Look at chapter 5 section 7 (5.7 in Numerical Recipes), there there is a treatment of numerical derivatives. It is basically the finite difference approach to approximate a derivative using difference (based on simple Taylors series expansions).

In Chapter 19, implicit methods are reviewed like simple relaxation and even multigrid.

It is true that not everything is written and the reader is left with something to do.

First write down the equations you have to solve. Chose (for example) the Crank-Nicholson scheme for the time dependence (19.2-19.3 in the book). Then write the equations in difference forms (where the derivatives are expressed as differences). Then use a given method to solve the difference equations (you can use for example either direct matrix inversion, or a simple relaxation scheme or even a more advance multigrid method - also chapter 19).

If this is your first time with CFD and finite difference and implicit methods, then you might want to get some basic help from a colleague. Numerical Recipes is a good book to build and write your code and it is a very good starting point. And that's the only one I know online.

Let me know if chapter 5 and 19 help.

Cheers, Patrick.
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