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

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.

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

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.

"Compatibility means deliberately repeating other people's mistakes."
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JohnLeM
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Re: Monotone Schemes: what are they and why are they good?

@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.

Cuchulainn
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Joined: July 16th, 2004, 7:38 am
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Re: Monotone Schemes: what are they and why are they good?

@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

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.