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Unformatted text preview: 2 2 u tt ( x i , 0); from the equation, u tt ( x i , 0) = c 2 u xx ( x i , 0) = c 2 f 00 ( x i ) ≈ c 2 ( f ( ih )-2 f (( i-1) h ) + f (( i-2) h )) /h 2 . Then, for each j +1 = 3 ,...,N , (1) is a linear system for the unknown vector ( u 2 ,j +1 ,...,u M,j +1 ), and all you need is to solve this system. The matrix A of this system is of size ( M-1) × ( M-1), with 2(1+ m 2 ) on the main diagonal,-m 2 just above and below the main diagonal, and 0 elsewhere. If you write U ( j ) for the vector-column ( u 2 ,j ,...,u M-1 ,j ), then the system to solve is AU ( j + 1) = 4 U ( j )-AU ( j-1) ....
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This note was uploaded on 10/06/2009 for the course MATH 445 taught by Professor Friedlander during the Fall '07 term at USC.
- Fall '07