{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# 11 geometry for the collocation solution of 911

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: ion solution of (9.1.1) showing the restriction of the cubic Hermite polynomial basis to the subinterval x 1 x ]. i; i In order to obtain approximate solutions of (9.1.1) using (9.1.2), we collocate at two points 1, 2 per subinterval and satisfy the boundary conditions. Thus, the unknown coe cients c , d , i = 0 1 ::: N , are determined as the solution of i i i i LY ( ) = r( ) ij j=1 2 ij Y (a) = A i = 1 2 ::: N (9.1.3a) Y (b) = B: (9.1.3b) The restriction of (9.1.2a) to the subinterval x 1 x ) is i; Y (x) = c i; 1 3 i; i 3 3 3 1 (x) + d 1 ! 1 (x) + c (x) + d ! (x): i; i i; Substituting (9.1.4) into (9.1.3a) LY ( 1) = L c 1 + R c = r( 1) LY ( 2) d1 d r( 2) where 3 3 3 L = L 3 1( 1) L!3 1( 1) R = L 3( L 1( 2) L! 1( 2) L( With (9.1.4), the boundary conditions (9.1.3b) become i i; i i i i; i i; i i i i; i; i i; i i c L0 d00 = A R 2 N +1 c d N N i i i i (9.1.4) i = 1 2 ::: N i i i i i i (9.1.5a) L!3( 1) : L!3( 2) (9.1.5b) 1) 2) =B i i i i (9.1.6a) where L0 = R N 1 0]: +1 = Combining (9.1.5) and (...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online