Timeline for Nonlinear Robin boundary condition involving square root
Current License: CC BY-SA 4.0
8 events
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| Jan 7, 2023 at 14:33 | comment | added | mathemania |
I see, I filled the code with comments so that it'll be easier to read for non-Mathematica users. In any case, I did exactly what is in your post (it's in the Newton's method part of my code). I first set up the equations, then prepare the finite difference and the residuals which is the $b$ in $\textbf{A} \vec{z} = \vec{b}$ (and the partials of the residual is the Jacobian matrix $\textbf{A}$), then create the sparse matrix, then Newton's method.
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| Jan 7, 2023 at 14:13 | comment | added | ConvexHull | Ok, I see the problem. In general, the consistence checks should be fullfilled, pointwise (using a FD method). However, I am no Mathematica user, so I am not able to debug the code. I must think about it a bit. | |
| Jan 7, 2023 at 14:08 | comment | added | mathemania | I didn't say anything that $z(x=a) = 0$, what I'm saying is that looking at the Robins condition where all terms are on one side so that it is an equation (something = 0). I have written my code in such a way too so that if you check everything, the result should give 0 (of course machine precision zero), i.e. it satisfies the Robins condition. | |
| Jan 7, 2023 at 13:46 | comment | added | mathemania | You mean it is correct to use the same way of discretizing as in the simpler setup that I wrote? But, in the last part of my code you can see that the solution I got doesn't really satisfy the governing equation and the boundary condition, i.e. it's not equal to 0. | |
| Jan 7, 2023 at 13:43 | comment | added | ConvexHull | Of course, your problem simply boils down to a linear discretization of the Poisson problem using Robin boundary conditions. | |
| Jan 7, 2023 at 13:43 | comment | added | mathemania | That is exactly how I solved the problem (I added a Mathematica the code with comments), however, I'm not sure if writing the Robins condition in the same way is correct, i.e. like the simpler setup I wrote at the start of my post. | |
| Jan 7, 2023 at 13:37 | history | edited | ConvexHull | CC BY-SA 4.0 |
deleted 6 characters in body
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| Jan 7, 2023 at 13:28 | history | answered | ConvexHull | CC BY-SA 4.0 |