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**1. The problem statement, all variables and given/known data**

Differential operator L ir approximated with a positively defined difference operator [tex]\Lambda[/tex]>0, that has a full special-function (λ) and special-value set and 0<λ

_{min}<λ<λ

_{max}. Explore the numerical stability in relation to the initial conditions s and right-hand side function w of the following difference schemes:

[tex]\frac{y^{n+1}_{i}-y^{n}_{i}}{\tau}[/tex]-k[tex]\Lambda[/tex][tex]\frac{y^{n+1}_{i}-y^{n}_{i}}{2}[/tex]=[tex]w^{n}_{i}[/tex]; [tex]y^{0}_{i}[/tex]=[tex]s_{i}[/tex]

if k - a given constant and w - a given function of the grid.

**2. Relevant equations**

Any basic explanations as to what is what will do as I am extreemly clueless in this entire ordeal.

I will take

*any*help I can get if anybody is willing.

**3. The attempt at a solution**

I haven't had one yet and based on previous experience in this subject, all my attempts would be very, very futile and very, very wrong.