|Oct7-12, 11:17 PM||#1|
Request for Hints to solve a Non-Linear PDE
Would you please provide me with some hints to find the analytical solution of the non-linear PDE given below:
BC's and IC's are:
Uz(0,t)=A*H(t); "H" is the heaviside function and H(0)=0
where A, B, and C are constant.
|Oct9-12, 02:38 AM||#2|
Since there is no answer yet to the question, I dare give my opinion on the subject.
The analytical solutions of most of the non-linear PDE are not known. The solutions of only a few of them can be formally expressed (generally in case of school problems). In practice, numerical methods are used to treat the problems involving PDE in physics or industry.
I think that the mohammad449's non-linear PDE should be treated with a numerical software.
Nevertheless, I hope that someone will give a more theoretical answer.
|Oct9-12, 05:37 AM||#3|
Thanks so much Dear JJacquelin!
Actually, the original equation has been simplified to the given form. I have the numerical results of the original complicated equation.
Currently, I am trying to find an analytical solution to match the numerical one. I tried the Heat Integral method (to get an approximation) but the resulting solution was not accurate enough, it just works in some specific conditions.
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