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Cuchulainn
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Re: Monotone Schemes: what are they and why are they good?

October 12th, 2020, 9:41 pm

Samarski on 2-factor monotone schemes (nice idea, but it doesn't work.. constraint 3.21 is impossible). You can get it monotone but I'm not telling.

http://samarskii.ru/articles/2002/2002-003.pdf

Roelof does a better job.

Back to barracks

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Cuchulainn
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Re: Monotone Schemes: what are they and why are they good?

October 15th, 2020, 8:31 pm

This thread is reaching a potential cul-de-sac. Here is CN versus ADE for UVM model.

And the wiggles get bigger for delta and gamma.


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JohnLeM
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Re: Monotone Schemes: what are they and why are they good?

November 30th, 2020, 6:54 pm

@Cuchulainn : I am reading a quite good book over these topics : Matrix Iterative Analysis by Richard S. Varga. It is a book from 1962, updated in 1999. The whole chapter 3 is dedicated to M and H matrices, Chapter 8 to their use in parabolic problems.
You should appreciate most of the other chapter : chap 7 on alternate directions and so on.
 
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Cuchulainn
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Re: Monotone Schemes: what are they and why are they good?

November 30th, 2020, 7:51 pm

@Cuchulainn : I am reading a quite good book over these topics : Matrix Iterative Analysis by Richard S. Varga. It is a book from 1962, updated in 1999. The whole chapter 3 is dedicated to M and H matrices, Chapter 8 to their use in parabolic problems.
You should appreciate most of the other chapter : chap 7 on alternate directions and so on.
Yes. Part of my PhD thesis in 1980 used some of the results. > 40 years ago Image

You might like this article
http://samarskii.ru/articles/2002/2002-003.pdf

Ideally, you want [$]h_1[$] and [$]h_2[$] constant, so take [$]x = log(S_1)[$] etc. in typical 2d pde and see how things work out real nice. As an exercise :-)

[$]\rho/\sigma \le h_1/h_2 \le (\rho\sigma)^{-1}[$] in the case of Heston.

JM: what's it for a spread option?
The CRUX is getting equation 3.21 up and running, it's necessary and sufficient for monotonicity.
"Compatibility means deliberately repeating other people's mistakes."
David Wheeler

http://www.datasimfinancial.com
http://www.datasim.nl