Consider the boundary-value problem 02 u 0x 2 02 u 0y2 0, 0 , x , 2, 0 , y , 1 u(0, y)
Chapter 16, Problem 1(choose chapter or problem)
Consider the boundary-value problem
\(\frac{\partial^{2} u}{\partial x^{2}}+\frac{\partial^{2} u}{\partial y^{2}}=0\), 0<x<2, 0<y<1
u(0, y)=0, u(2, y)=50, 0<y<1
u(x, 0)=0, u(x, 1)=0, 0<x<2
Approximate the solution of the differential equation at the interior points of the region with mesh size \(h=\frac{1}{2}\). Use Gaussian elimination or Gauss–Seidel iteration.
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