# 324a may easily be solved by forward and backward

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## This document was uploaded on 03/16/2014 for the course CSCI 6860 at Rensselaer Polytechnic Institute.

Ask a homework question - tutors are online