Question on Numerical methods- How do I use programming to solve discretion problems?

[maggiegold]

I am given this question- I'm stuck with using programming to solve discretion problems
Question 1a) Express Tij @ t+1 = F(Ti+1,j, Ti-1,j, Ti,j+1, Ti,j-1) at t explicitly, then advance in time
Question 1b)
Suppose, there is no t variable, now what? Make a guess!
Ideally: F(Ti,j, Ti+1,j , Ti-1,j, Ti,j+1, Ti,j-1)=0
With guessed values: F(Ti,j, Ti+1,j , Ti-1,j, Ti,j+1, Ti,j-1)= err(/=0)
Objective is to reduce error as much as possible
Requirements
Write down discretized equations(interior, boundary)- explicit, implicit?
Specify what algorithms are used and how to program?




This problem is continued at:

I ask this question before. Now giving the updates on the question about discretization problem

Older post reference: https://www.freemathhelp.com/forum/threads/question-on-numerical-methods-how-do-i-use-programming-to-solve-discretion-problems.127729/#post-524836 I am given this question- I'm stuck with using programming to solve discretion problems For Question 1a), I am given that...

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[HallsofIvy]

Frankly this problem makes no sense to me. It makes no sense to have "T" as the variable for both horizontal and vertical axes. Also, it makes no sense to have \(\displaystyle T_{ij}\) as a function of \(\displaystyle T_{ij}\) for different i and j. I suspect it should be \(\displaystyle F(T_{ij})\) that is to be approximated by \(\displaystyle \frac{F(T_{ij+1})+ F(T_{i+1j})+ F(T_{ij-1})+ F(T_{i-1j})}{4}\).

 

[maggiegold]

I think the objective is to reduce error as much as possible, i think your suspicion is right. the question is badly phrased. I also don't understand.

This problem is continued at:

I ask this question before. Now giving the updates on the question about discretization problem

Older post reference: https://www.freemathhelp.com/forum/threads/question-on-numerical-methods-how-do-i-use-programming-to-solve-discretion-problems.127729/#post-524836 I am given this question- I'm stuck with using programming to solve discretion problems For Question 1a), I am given that...

www.freemathhelp.com

 

[Deleted member 4993]

Frankly this problem makes no sense to me. It makes no sense to have "T" as the variable for both horizontal and vertical axes. Also, it makes no sense to have \(\displaystyle T_{ij}\) as a function of \(\displaystyle T_{ij}\) for different i and j. I suspect it should be \(\displaystyle F(T_{ij})\) that is to be approximated by \(\displaystyle \frac{F(T_{ij+1})+ F(T_{i+1j})+ F(T_{ij-1})+ F(T_{i-1j})}{4}\).

T is the variable in "z" direction. The T=0 and T=1 are the boundary conditions.