Can we solve this on MATLAB?

∇∙k(x,y)∇T+Q=0 on OMEGA

T=x on y=0

T=3+x^2 on y=3

T=y on x=0

∂T/∂x=1-T/5 on x=3

[Rashmin Rayani]

k=1

[Daniel M]

Yes. What have you tried?

[Rashmin Rayani]

have done it theoretically but don't actually know how put that in code or how to start with this kind of problems

Answer 1

[Prabhan Purwar]

Following equation can be solved by making use of curl() and vpasolve() functions, as shown in the below example code:

syms x y z
V = [x^3*y^2*z, y^3*z^2*x, z^3*x^2*y];
X = [x y z];
curl(V,X)
S = vpasolve(curl(V,X)+X == 0, x,y,z);
double(S.x)

ans =

   0.0000 + 0.0000i
  -1.0000 + 0.0000i
   1.0000 + 0.0000i
   0.0000 - 1.0000i
   0.0000 + 1.0000i

Please have a look at the following code representing the working of solve and assume functions to solve equations with conditions.

https://www.mathworks.com/matlabcentral/answers/480574-solve-equations-with-constraints

Please refer to the following link for further information

• https://www.mathworks.com/help/symbolic/curl.html(Curl)
• https://www.mathworks.com/help/matlab/ref/divergence.html(Divergence)
• https://www.mathworks.com/help/symbolic/vpasolve.html(Vpasolve)

Hope this helps.