Please advise the to the answer

[PA3040D]

Could you please review the attached image for the question and my answer? I've marked the boundary conditions according to the provided instructions, but there are four additional positions where I'm unsure about setting the boundary conditions. Can you advise on how to set the boundary conditions for these remaining locations? Additionally, could you please confirm whether the marked boundary conditions are correct or incorrect?

 

[khansaheb]

Could you please review the attached image for the question and my answer? I've marked the boundary conditions according to the provided instructions, but there are four additional positions where I'm unsure about setting the boundary conditions. Can you advise on how to set the boundary conditions for these remaining locations? Additionally, could you please confirm whether the marked boundary conditions are correct or incorrect?

View attachment 37704

View attachment 37703

Please re-draw another square and "assign" letters to each intersection points and indicate their co-ordinate - knowing h= 1/3. For example:

O(0,0)

The top-right-corner (intersection) - you can call it R and its co-ordinate is (1,1) ..... and continue)

 

[PA3040D]

Please re-draw another square and "assign" letters to each intersection points and indicate their co-ordinate - knowing h= 1/3. For example:

O(0,0)

The top-right-corner (intersection) - you can call it R and its co-ordinate is (1,1) ..... and continue)

Grate Thanks for the reply and help
ABCD pints boundary conditions are the issue
Please help

 

[khansaheb]

Grate Thanks for the reply and help
ABCD pints boundary conditions are the issue
Please help
View attachment 37708

How did you get the y-coordinate of F to be 1/2 ? Check it again.

 

[PA3040D]

How did you get the y-coordinate of F to be 1/2 ? Check it again.

Yes Thanks it should be corrected that is my mistake

This is correct one...... but still I did not understand how boundary conditions are set

 

[mario99]

Yes Thanks it should be corrected that is my mistake

This is correct one...... but still I did not understand how boundary conditions are set

View attachment 37714

The aim is to find $u_1$, $u_2$, $u_3$, and $u_4$ which are located at the interior points $P_{12}$, $P_{22}$, $P_{11}$, and $P_{21}$, respectively.

We need to construct $4$ equations since we have $4$ unknows. Now if we apply the central difference equation to the point $P_{11}$, we get the first equation:

$u_{21} + u_{12} + u_{01} + u_{10} - 4u_{11} = 0$

$u_{21} = u_4$, $u_{12} = u_1$, and $u_{11} = u_3$ are some of the points that you want to find while $u_{10} = P_{10}$ is one of the boundary points that you have already found. ($P_{10} = 1$)

You don't understand how boundary conditions are set to find the boundary points? Is that what you mean by your question? If yes, let us find again the boundary point $P_{10}$. I think that this will be a good example to understand the idea.

$P_{10} = P(h, 0) = P(\frac{1}{3},0) = \ ?$

Now look at the boundary conditions. Does it tell us anything when $x = \frac{1}{3}$? No. Does it tell us anything when $y = 0$? Yes. Then, $P_{10} = 1$.

 

[Dr.Peterson]

Could you please review the attached image for the question and my answer? I've marked the boundary conditions according to the provided instructions, but there are four additional positions where I'm unsure about setting the boundary conditions. Can you advise on how to set the boundary conditions for these remaining locations? Additionally, could you please confirm whether the marked boundary conditions are correct or incorrect?

View attachment 37704

View attachment 37703

You asked about the same problem a year ago:

Please help to solve this problem: u=f(x,y) satisfies d^2u/dx^2 + d^u/dy^2 = 0 in 0<x<1, 0<y<1, with...

Please help to solve this problem Pleaee

www.freemathhelp.com

What has happened over the last year? Are you still taking the same course?

 

[PA3040D]

You asked about the same problem a year ago:

Please help to solve this problem: u=f(x,y) satisfies d^2u/dx^2 + d^u/dy^2 = 0 in 0<x<1, 0<y<1, with...

Please help to solve this problem Pleaee

www.freemathhelp.com

What has happened over the last year? Are you still taking the same course?

Yes This is second time

 

[PA3040D]

The aim is to find $u_1$, $u_2$, $u_3$, and $u_4$ which are located at the interior points $P_{12}$, $P_{22}$, $P_{11}$, and $P_{21}$, respectively.

We need to construct $4$ equations since we have $4$ unknows. Now if we apply the central difference equation to the point $P_{11}$, we get the first equation:

$u_{21} + u_{12} + u_{01} + u_{10} - 4u_{11} = 0$

$u_{21} = u_4$, $u_{12} = u_1$, and $u_{11} = u_3$ are some of the points that you want to find while $u_{10} = P_{10}$ is one of the boundary points that you have already found. ($P_{10} = 1$)

You don't understand how boundary conditions are set to find the boundary points? Is that what you mean by your question? If yes, let us find again the boundary point $P_{10}$. I think that this will be a good example to understand the idea.

$P_{10} = P(h, 0) = P(\frac{1}{3},0) = \ ?$

Now look at the boundary conditions. Does it tell us anything when $x = \frac{1}{3}$? No. Does it tell us anything when $y = 0$? Yes. Then, $P_{10} = 1$.

Dear Sir Grate thanks for the reply and details explanation

Now I got the grate logic how find the boundary values using give expression

Thanks again and again


Can you please help me to understand boundary values for following scenario which has less information's

 

[mario99]

Dear Sir Grate thanks for the reply and details explanation

Now I got the grate logic how find the boundary values using give expression

Thanks again and again


Can you please help me to understand boundary values for following scenario which has less information's

View attachment 37719

Could you please post this problem in a new thread because we are allowed to solve one problem in one thread?

 

[PA3040D]

The aim is to find $u_1$, $u_2$, $u_3$, and $u_4$ which are located at the interior points $P_{12}$, $P_{22}$, $P_{11}$, and $P_{21}$, respectively.

We need to construct $4$ equations since we have $4$ unknows. Now if we apply the central difference equation to the point $P_{11}$, we get the first equation:

$u_{21} + u_{12} + u_{01} + u_{10} - 4u_{11} = 0$

$u_{21} = u_4$, $u_{12} = u_1$, and $u_{11} = u_3$ are some of the points that you want to find while $u_{10} = P_{10}$ is one of the boundary points that you have already found. ($P_{10} = 1$)

You don't understand how boundary conditions are set to find the boundary points? Is that what you mean by your question? If yes, let us find again the boundary point $P_{10}$. I think that this will be a good example to understand the idea.

$P_{10} = P(h, 0) = P(\frac{1}{3},0) = \ ?$

Now look at the boundary conditions. Does it tell us anything when $x = \frac{1}{3}$? No. Does it tell us anything when $y = 0$? Yes. Then, $P_{10} = 1[/imaDear Sir, attached to the link below is a new post related to my second question. I believe you would be the most suitable person to provide an answer to these questions. Please take a moment to review the question at your convenience." [/QUOTE]$

The aim is to find $u_1$, $u_2$, $u_3$, and $u_4$ which are located at the interior points $P_{12}$, $P_{22}$, $P_{11}$, and $P_{21}$, respectively.

We need to construct $4$ equations since we have $4$ unknows. Now if we apply the central difference equation to the point $P_{11}$, we get the first equation:

$u_{21} + u_{12} + u_{01} + u_{10} - 4u_{11} = 0$

$u_{21} = u_4$, $u_{12} = u_1$, and $u_{11} = u_3$ are some of the points that you want to find while $u_{10} = P_{10}$ is one of the boundary points that you have already found. ($P_{10} = 1$)

You don't understand how boundary conditions are set to find the boundary points? Is that what you mean by your question? If yes, let us find again the boundary point $P_{10}$. I think that this will be a good example to understand the idea.

$P_{10} = P(h, 0) = P(\frac{1}{3},0) = \ ?$

Now look at the boundary conditions. Does it tell us anything when $x = \frac{1}{3}$? No. Does it tell us anything when $y = 0$? Yes. Then, $P_{10} = 1$.

Dear Sir, attached to the link below is a new post question that related to this question . I believe you would be the most suitable person to provide an answer to these questions. Please take a moment to review the question at your convenience.

https://www.freemathhelp.com/forum/threads/please-help-to-find-the-answer.138147/