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I am trying to solve this equation (numerically)

$$\dfrac{\partial u}{\partial t}=\dfrac 3 x\dfrac \partial{\partial x}\left(\sqrt x \frac \partial {\partial x}(\nu(u,u^2,\cdots,u^k)u\sqrt x)\right)$$ And its expanded form:

$$u_t=3\nu(u,u^2,\cdots)u_{xx}+\left(6\nu_x(u,u^2,\cdots)+\dfrac{3\nu(u,u^2,\cdots)}{2x}\right)u_x+\left(\nu_x(u,u^2,\cdots)\left(3+\dfrac 1 {2x}\right)+\dfrac{3\nu(u,u^2,\cdots)}{x}\right)$$

Where $u$ is a function of $u=u(t,x)$. ($\nu$ a is a nonlinear function of $u$, but the truth is that $\nu$ is that and besides is a function of other variable. But but for a given $u$ I can obtain it. So I decided not put that here for simplicity)

What do you think that is the better way (most stable fastest an accurate) to solve this? I was trying MOL in matlab, but I am really stuck.

Help please.

share|improve this question
You should also check out Computational Science. –  user2468 Apr 2 '12 at 12:55
I will. Thanks. –  Nikko Apr 2 '12 at 15:55

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