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

In summary, the conversation is about a difficult subject that the speaker is struggling with and has not been able to pass. They are seeking help with a specific problem related to differential and difference operators and numerical stability. They admit to being clueless and willing to take any help they can get.
  • #1
Thorra
45
0
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 [itex]\Lambda[/itex]>0, that has a full special-function (λ) and special-value set and 0<λmin<λ<λmax. Explore the numerical stability in relation to the initial conditions s and right-hand side function w of the following difference schemes:
[itex]\frac{y^{n+1}_{i}-y^{n}_{i}}{\tau}[/itex]-k[itex]\Lambda[/itex][itex]\frac{y^{n+1}_{i}-y^{n}_{i}}{2}[/itex]=[itex]w^{n}_{i}[/itex]; [itex]y^{0}_{i}[/itex]=[itex]s_{i}[/itex]
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.
 
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  • #2
May I bump this question? Cause I need some help of any kind...
 
  • #3
Do you not know the basic definitions? In particular, what is the specific definition of "numerical stability in relation to the initial conditions"?
 

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

What is numerical analysis?

Numerical analysis is a branch of mathematics that deals with the development and implementation of algorithms and computational methods to solve mathematical problems that cannot be solved analytically.

What is the purpose of numerical analysis in homework assignments?

The purpose of numerical analysis in homework assignments is to develop and improve students' problem-solving skills by applying numerical methods and algorithms to solve complex mathematical problems.

What are some common numerical analysis techniques used in homework assignments?

Some common numerical analysis techniques used in homework assignments include root finding, interpolation, numerical integration, and solving differential equations.

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Numerical analysis methods can be applied in various fields such as engineering, physics, economics, and computer science to solve real-life problems that involve complex mathematical calculations.

What are some challenges students may face when completing numerical analysis homework?

Some common challenges students may face when completing numerical analysis homework include understanding the underlying mathematical concepts, implementing the algorithms correctly, and dealing with large datasets or complex problems.

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