What to produce for the numerical solutions portions, that is, what step sizes to implement in...

 

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What to produce for the numerical solutions portions, that is, what step sizes to implement in space and time, what to display and what to provide as printouts. Use the step size combinations k below to solve each of the PDE's. Recall that r= when the PDE is elliptic. h du d'u Numerical Problem 1. The function u satisfies Laplace's equation, + -=0 at the points dx dy² of the square 0<x<4, 0<y<4 and the Dirichlet boundary conditions: u(x, y) = 0, along x = 0; u(x, y) = 0, along y = 0; u(x, y)=x², y=4, 0<x<4; u(x, y) linear and continuous along x =4, 0≤y≤4 What to produce for the numerical solutions portions, that is, what step sizes to implement in space and time, what to display and what to provide as printouts. Use the step size combinations k below to solve each of the PDE's. Recall that r= when the PDE is elliptic. h du d'u Numerical Problem 1. The function u satisfies Laplace's equation, + -=0 at the points dx dy² of the square 0<x<4, 0<y<4 and the Dirichlet boundary conditions: u(x, y) = 0, along x = 0; u(x, y) = 0, along y = 0; u(x, y)=x², y=4, 0<x<4; u(x, y) linear and continuous along x =4, 0≤y≤4

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To solve Laplaces equation 2 ux 2 2 uy 2 0 numerically with the given Dirichlet boundary conditions ... View the full answer