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math572_hw6

# math572_hw6 - MATH 572 Numerical Methods for Scientific...

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Unformatted text preview: MATH 572 Numerical Methods for Scientific Computing II Winter 2005 Assignment #6 due : Thursday, April 7 1. Consider the heat equation in two dimensions, v t = v xx + v yy , on the domain 0 ≤ x, y ≤ 1 with Dirichlet boundary conditions v (0 , y, t ) = v (1 , y, t ) = v ( x, , t ) = 0 , v ( x, 1 , t ) = 1 and initial condition v ( x, y, 0) = 0. The solution v ( x, y, t ) represents the temperature of a square plate that is heated on one side and cooled on the other three sides. Solve the problem numerically up to time t = 2 using the explicit scheme u n +1 j,l = u n j,l + k ( D x + D x- + D y + D y- ) u n j,l . Take h = 0 . 1 and k = 0 . 0025. Make a contour plot and a surface plot of the numerical solution at time t = 2 (including the boundary values). The relevant commands in Matlab are contour and mesh (or surf ). 2. Fritz John wrote in his textbook on partial differential equations, “Instability of a difference scheme under small perturbations does not exclude the possibility that in special...
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