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These are replies submitted by Oliveira

hello acer.
My recovery was not good. Follow the attached file.


I'll check out the FAQs and try to make a fix. Thank you Thomas for your attention.

This procedure worked. Thanks for the tip Carl.

Indeed, the gradient of a vector field is a tensor. I also didn't find a function that performed this procedure. Thank you for your attention tomleslie.

I applied this procedure and the appearance was good. Thanks Scot for the tip.

It really looks complicated.
Thank you for your acer.

It's good to share doubts too. Thank you all.


This is what I was needing. Thank you for your attention Carl.


Works well. Thanks again for the help acer.

I also thank you all for your attention.

I've also seen something similar to Dirichlet Conditions.



This approach is more complicated. I will change the plate to a rectangular shape. Again, I am grateful for the information Rouben.

PDE := diff(u(x, y), x, x)+diff(u(x, y), y, y) = 0

diff(diff(u(x, y), x), x)+diff(diff(u(x, y), y), y) = 0


BC := {u(0, y) = 20, u(2, y) = 100, u(x, 0) = 0, u(x, 1) = piecewise(x <= 1, 20, 100)}


pdsolve([PDE, op(BC)], u(x, y))

u(x, y) = Sum((160*sin((1/2)*n*Pi*x)*(cos((1/2)*Pi*n)-(5/4)*(-1)^n+1/4)*exp(-(1/2)*Pi*n*(y-9))-160*sin((1/2)*n*Pi*x)*(cos((1/2)*Pi*n)-(5/4)*(-1)^n+1/4)*exp(-(1/2)*Pi*n*(y-1))+160*sin((1/2)*n*Pi*x)*(cos((1/2)*Pi*n)-(5/4)*(-1)^n+1/4)*exp((1/2)*Pi*n*(y+1))-160*sin((1/2)*n*Pi*x)*(cos((1/2)*Pi*n)-(5/4)*(-1)^n+1/4)*exp((1/2)*Pi*n*(y+9))-40*sin(n*Pi*y)*((-1)^n-1)*(exp(Pi*n*(x+1))+5*exp(Pi*n*(x+2))-5*exp(Pi*n*(x+3))-exp(-Pi*n*(x-5))+exp(-Pi*n*(x-4))+5*exp(-Pi*n*(x-3))-5*exp(-Pi*n*(x-2))-exp(n*Pi*x)))/((-exp(5*Pi*n)+exp(4*Pi*n)+exp(Pi*n)-1)*n*Pi), n = 1 .. infinity)



In symbolic form, Maple returns a closed solution.


Download pde.mw

When I evaluate, Maple returns the following message:

Error, (in pdsolve/numeric) unable to handle elliptic PDEs.

Indeed, pdsolve cannot numerically solve elliptical pdes.

Thank you for your attention mmcdara. I will try to apply this procedure, because I also have little experience with Maple.

Thanks also to Rouben for the comment.

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