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4. Consider the nonlinear PDE in two dimensions given by rau au ax2 * ay2 te= g(x,y). Here u = u(x,y) is a function in

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4. Consider the nonlinear PDE in two dimensions given by rau au ax2 * ay2 te"= g(x,y). Here u = u(x,y) is a function in the two variables x and y, defined on the unit square (0.1) (0.1) and subject to homogeneous Dirichlet boundary conditions. We discretize it on a uniform mesh, just like in Example 7.1, using h=1/(N+1), and obtain the equations 4ui,j-w1+1,7 Wi-1; -11.j+1 11,5-1+hemi = h 81.), 1sij<>

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