## Lemma questions

A Partial Differential Equation Approach

### Lemma questions

In lemma 11.1 on P129 you state that L_h^k \omega \leq 0 on the interior of the mesh. Given that is satisfies the approximation of the balck scholes equation is if fair to asume that L_h^k \omega = 0 on the interior of the mesh?

also in Leema 11.2

If first says suppose that max |U_j^n| \leq N for all j and n

and max|f_j^n| leq N for all j and n

firstly is the 2nd term not redundant? Plust by making this assumption are we not effectively assuming stability rather than proving it?

Also comparing equation 3.13 on page 28 with lemma 11.12 the max seems to have been replaced by a + rather than a max function is moving from continuous to discrete time why was this?
Bazman76

Posts: 5
Joined: Tue Aug 17, 2010 2:30 pm

""In lemma 11.1 on P129 you state that L_h^k \omega \leq 0 on the interior of the mesh. Given that is satisfies the approximation of the balck scholes equation is if fair to asume that L_h^k \omega = 0 on the interior of the mesh?

also in Leema 11.2 ""

The omega can be any function. Similar techniques can be seen here for calculating the far field

http://www.math.cmu.edu/CNA/Publication ... NA-016.pdf

Cuchulainn

Posts: 676
Joined: Mon Dec 18, 2006 2:48 pm
Location: Amsterdam, the Netherlands

Ah that answers teh first part.

Can you shed any light on the second?
Bazman76

Posts: 5
Joined: Tue Aug 17, 2010 2:30 pm

Thank Baz;

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"also in Leema 11.2

If first says suppose that max |U_j^n| \leq N for all j and n

and max|f_j^n| leq N for all j and n

firstly is the 2nd term not redundant? Plust by making this assumption are we not effectively assuming stability rather than proving it? "

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Attachments
exponentialfitting_415.pdf

Cuchulainn

Posts: 676
Joined: Mon Dec 18, 2006 2:48 pm
Location: Amsterdam, the Netherlands

ah thanks for this!
Bazman76

Posts: 5
Joined: Tue Aug 17, 2010 2:30 pm

### Re: Lemma questions

hi,
How would you implement a sparsed matrix using just the standard STL containers? anyone explain it.
sabahat

Posts: 1
Joined: Tue Nov 11, 2014 8:59 am