Question: Diffusion Equation - inverse solution for finding the diffusion coefficient

Hello everyone

I have the solution of diffusion equation from Help of maple website. I put the code here


restart: with(plots):


alias(c[0]=c0, c[1]=c1, c[2]=c2);
IBC:={C(x,0)=cx0, C(0,t)=ct0, D[1](C)(10,t)=0};
L1:=[0.01, 0.1, 1, 5, 10];
L2:=[red, green, yellow, blue, magenta, black];
for i from 1 to 5 do
 pn[i] := pds:-plot(t=L1[i], color=L2[i]):
end do:
display({seq(pn[i], i=1..5)}, title=`Numerical solution at t=0.01, 0.1, 1, 5, 10`);



the code is working perfectly. But, My question is how can I found the diffusion constant (D) if I have the solution ( C(x,t) ).  Probably it should be an algorithm which use least square method to find (D) based on the data C(x,t).

I am looking for a fast and efficient algorithm if there is any.

thank you so much for your kind attentions in advance

Sincerely yours,


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