On 04/21/2018 03:06 AM, Pawan Kumar wrote:
$$u_t = u_{rr}+ \frac{1}{r} u_r - \frac{1}{r} \frac{\partial}{\partial r} (r
\lambda(u) \frac{\partial v}{\partial r}) +f(u,v)$$
$$v_t = v_{rr} + \frac{1}{r} v_r + g(u,v) $$
But at $r=0$, it becomes :
$$u_t = 2u_{rr}-2uv_{rr}-u_r h_r +f(u,v)$$
$$v_t = 2v_{rr}+g(u,v)$$
So, my doubts are:
1. Since, its a time dependent, vector valued \& non-linear set of PDEs, which
tutorials should I follow to solve these? I found 21, 26, 31 \& 31 related
but some of them are too complicated, is there any relatively simpler way !! \\
You just have a system of coupled heat equations. 21, 26, 22 seems like a
reasonably choice.
2. How to handle the condition at $r=0$ with the homogeneous Neumann BC?
You don't have to do anything special if you don't just multiply by a test
function (say, w(r)) and then integrate over r=0...R, but if you also multiply
by a weight factor 2*pi*r. So, for example, out of the u_t term, you'll get
\int_{r=0}^R w(r) u_t(r) 2*pi r dr
This way, the singularity disappears in all relevant terms.
Best
W.
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Wolfgang Bangerth email: [email protected]
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