Use the finite difference method to find the solution u(x, y) of the following Poisson's equation:...

 

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Use the finite difference method to find the solution u(x, y) of the following Poisson's equation: + x2 au y2 =-6-xy (1) in the rectangle 0 < x < 2,0 < y < 1 that satisfies the following Dirichlet boundary conditions: u(x, 0) = x - 2x, u(x, 1) = x (x -. x (x - 1/3) u(0,y) = 4y(1 y), u(2, y) = 4y (1 y 2) (2) (3) a. Compute the solution assuming equidistant grid points with h = 0.25 (for both axes). Draw a surface plot of the numerical approximation to the solution. Use the finite difference method to find the solution u(x, y) of the following Poisson's equation: + x2 au y2 =-6-xy (1) in the rectangle 0 < x < 2,0 < y < 1 that satisfies the following Dirichlet boundary conditions: u(x, 0) = x - 2x, u(x, 1) = x (x -. x (x - 1/3) u(0,y) = 4y(1 y), u(2, y) = 4y (1 y 2) (2) (3) a. Compute the solution assuming equidistant grid points with h = 0.25 (for both axes). Draw a surface plot of the numerical approximation to the solution.