2 to nonlinear problems y f x y 0 glya 0 axb gr

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ting these results into (7.3.1) and neglecting the O( y2) terms y + y = f (x y) y + f (x y) 0 or 0 y y = f (x y) y + f (x y) ; y : 0 0 y This has the form of a linear system y = A(x) y + b(x) (7.3.3a) 0 with A(x) = f (x y) y b(x) = f (x y) ; y : 0 Linearizing the left boundary condition yields gL(y(a) + y(a)) = gL(y(a)) + gLy (y(a)) y(a) = 0: 18 (7.3.3b) This has the form of the linear boundary condition L y(a) = l (7.3.4a) with L = gLy (y(a)) l = ;gL (y(a)): (7.3.4b) At the right end, we have R y(b) = r (7.3.5a) with R = gRy (y(b)) r = ;gR (y(b)): (7.3.5b) The linearized system (7.3.3 - 7.3.5) may be solved by iteration using the procedures of Section 7.2 thus, 1. Beginning with an initial guess y(0) (x), 0 x 1, 2. Solve the linear system y ( ) = A( ) (x) y( ) + b( ) (x) 0 L( ) y( ) (a) = l( ) R( ) y( )(b) = r( ) where A( )(x) = f (x Y( ) ), etc. y 3. After each iteration, set y( +1) = y( ) + y( ) and repeat the procedure until convergence. The procedure is awkward since interpolation...
View Full Document

This document was uploaded on 03/16/2014 for the course CSCI 6820 at Rensselaer Polytechnic Institute.

Ask a homework question - tutors are online