Is Numerical Stability Affected by Initial Conditions in This Difference Scheme?

[Thorra]

Sorry, but this is the only subject I could not pass even if I gave it my all every day and night of the semester. And I will still surely fail this subject, but as a last resort I will try to post my problem here, hoping to get solution and maybe an explanation. Sorry if some of the phrasing might be confusing, I'm merely translating from my native language.

Homework Statement

Differential operator L ir approximated with a positively defined difference operator \Lambda>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:
\frac{y^{n+1}_{i}-y^{n}_{i}}{\tau}-k\Lambda\frac{y^{n+1}_{i}-y^{n}_{i}}{2}=w^{n}_{i}; y^{0}_{i}=s_{i}
if k - a given constant and w - a given function of the grid.

Homework 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.

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.


Edit: To further testiment my cluelessness of this subject, I have the urging suspicion I have posted this in the wrong forum category.

 

[Thorra]

May I bump this question? Cause I need some help of any kind...

 

[HallsofIvy]

Do you not know the basic definitions? In particular, what is the specific definition of "numerical stability in relation to the initial conditions"?