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.
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This document was uploaded on 03/16/2014 for the course CSCI 6860 at Rensselaer Polytechnic Institute.
- Spring '14