324a may easily be solved by forward and backward

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Unformatted text preview: agonal systems. The input to the procedure should be N and vectors containing the coe cients aj , bj , cj , fj , j = 1 2 : : : N . The procedure should output the solution X. The coe cients aj , bj , etc., j = 1 2 : : : N , should be replaced by uj , vj , etc., j = 1 2 : : : N , in order to save storage. If you want, the solution X can be returned in F. 2.4. Estimate the number of arithmetic operations necessary to factor A and for the forward and backward substitution process. 3. Consider the linear boundary value problem ;pu 00 + qu = f (x) 0<x<1 u(0) = u (1) = 0: 0 where p and q are positive constants and f (x) is a smooth function. 3.1. Show that the Galerkin form of this boundary-value problem consists of nding u 2 H01 satisfying A(v u) ; (v f ) = Z 1 (v pu + vqu)dx ; 0 0 Z 1 0 0 vfdx = 0 1 8v 2 H0 : For this problem, functions u(x) 2 H01 are required to be elements of H 1 and satisfy the Dirichlet boundary condition u(0) = 0. The Neumann boundary condition at x = 1 need not be satis ed by either u or v. 3.2. Int...
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This document was uploaded on 03/16/2014 for the course CSCI 6860 at Rensselaer Polytechnic Institute.

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