Differential Equations Solutions 173

Differential Equations Solutions 173 - , U ( i, j ) = ( C (...

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Chapter 30 Solutions: Case Study: Fast Solvers and Sylvester Equations: Both Sides Now CHALLENGE 30.1. Equating the ( j, k ) element on each side of the equation ( B y U + UB x )= F , we obtain f ( x j ,y k )= 1 h 2 ( u ( x j 1 ,y k )+2 u ( x j ,y k ) u ( x j +1 ,y k ) u ( x j ,y k 1 )+2 u ( x j ,y k ) u ( x j ,y k +1 )) , which is the same as equation ( k 1) n + j of ( A x + A y ) u = f . CHALLENGE 30.2. (a) Using MATLAB notation for subvectors, the algorithm is: for i =1: n , for j =1: n
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Unformatted text preview: , U ( i, j ) = ( C ( i, j ) L ( i, 1 : i 1) U (1 : i 1 , j ) U ( i, 1 : j 1) R (1 : j 1 , j )) / ( L ( i, i ) + R ( j, j )) end end The number of multiplications is n X i =1 n X j =1 ( i 1 + j 1) = n 2 ( n 1) , and the other operations are also easy to count. 183...
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This note was uploaded on 01/21/2012 for the course MAP 3302 taught by Professor Dr.robin during the Fall '11 term at University of Florida.

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