Solve the boundary-value problem 02 u 0r2 1 r 0u 0r 2 1 r2 u 02 u 0z 2 0, 0 , r , 1, 0
Chapter 14, Problem 17(choose chapter or problem)
Solve the boundary-value problem
\(\frac{\partial^{2} u}{\partial r^{2}}+\frac{1}{r} \frac{\partial u}{\partial r}-\frac{1}{r^{2}} u+\frac{\partial^{2} u}{\partial z^{2}}=0\), 0<r<1, 0<z<1
u(1, z)=0, 0<z<1
u(r, 0)=0, \(u(r, 1)=r-r^{3}\), 0<r<1
[Hint: See equation (12) in Section 5.3.]
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