HW4 assignment - you can compute the error during each...

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HW#4 EGM6341 Spring 2009 Due: 2/19, Thursday From the textbook by Atkinson : pp 496-503: #6a, #21, #23 pp 574-583: #2, #10b, #14, #18, #33 Additional Note on Problem #33: * Eqn. 2 u = g , ( 2 = 2 2 2 2 y x + ). (1) * Discretization: 2 , 1 , , 1 ) ( 2 x u u j i j i j i u + - - + + 2 1 , , 1 , ) ( 2 y u u j i j i j i u + - - + = g i,j (2) => Truncation error: ) ( . . 4 4 4 4 2 y x h E T u u + * If the exact solution is u ex = x 2 y 2 , the truncation error will become zero since 4 4 4 4 0 x u x y y + = . => Such an exact solution requires: g(x, y) = 2 u ex = 2( x 2 + y 2 ) u(0, y) = u(x,0) = 0. * Now you know the exact solution and you know that the truncation error is exactly 0,
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Unformatted text preview: you can compute the error during each iteration by comparing your iterative solution with the exact solution u ex = x 2 y 2 . * Error in iteration: We define an average L2-norm “error” between two iterations: 2 / 1 ) 1 2 1 2 1 , , ( 2 1 2 1 ) ( ∑ ∑--=---=-= n j i n j i u u ny j nx i ny nx n err...
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This note was uploaded on 04/23/2009 for the course EGM 6341 taught by Professor Mei during the Spring '09 term at University of Florida.

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