Lemma questions

[Bazman76]

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Also comparing equation 3.13 on page 28 with lemma 11.12 the max seems to have been replaced by a + rather than a max function is moving from continuous to discrete time why was this?

[Cuchulainn]

""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

[Bazman76]

Ah that answers teh first part.



Can you shed any light on the second?

[Cuchulainn]

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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This is indeed a typo; the correct answer is in lemma 2(see also lemma 1) in this article

[Bazman76]

ah thanks for this!

[sabahat]

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