Lecture+27--Relaxation+method+_+Nonlinear+system

Lecture+27--Relaxation+method+_+Nonlinear+system -...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
Relaxation Method HIGH BIRD CHECKLIST • If you know the target is going to be high, keep your muzzles higher than normal at the ready position. • Do not aim at the target. If you do you’ll miss behind. High birds often appear to be travelling slower than they really are, tempting you to aim. You must remember to swing the gun - and keep the muzzles moving after you’ve pulled the trigger.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Relaxation Method Relaxation (weighting) factor Gauss-Seidel method:  = 1 Over-relaxation 1 <  < 2 Under-relaxation 0 <  < 1 Successive Over-relaxation (SOR) (1 ) new n i i ew x x λ = + - old i x old i x new i x new i x ( ) new i new i x x + = - old old i i x x ( 1)( ) new i new new i i x x x = + - - old i x
Background image of page 2
SOR Iterations Assume x1 = x2 = x3 = 0, and  = 1.2 Example: First iteration + = - = - + = 12 / ) x 5 80 ( x 8 / ) x 6 45 ( x 4 / ) 2 x x ( x 1 3 1 2 3 2 1 [ ] [ ] = - × + × + × - = = - × - × + × - = - = - + × + × - = 7 . 7 12 / ) 6 . 0 ( 5 80 2 . 1 0 ) 2 . 0 ( x 29 . 7 8 / ) 6 . 0 ( 6 45 2 . 1 0 ) 2 . 0 ( x 6 . 0 4 / ) 2 0 0 ( 2 . 1 0 ) 2 . 0 ( x 3 2 1 ( 29 Seidel - Gauss : S - G x 1 x x old i S G i i ; λ - + = -
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
SOR Iterations Second iteration Third iteration Converges slower !! (see MATLAB solutions) There is an optimal relaxation parameter = + × + × - = = - × + × - = = - + × + - × - = 4685 . 8 12 / )) 017 . 4 ( 5 80 ( 2 . 1 ) 7 . 7 ( ) 2 . 0 ( x 6767 . 1 8 / )) 017 . 4 ( 6 45 ( 2 . 1 ) 29 . 7 ( ) 2 . 0 ( x 017 . 4 4 / ) 2 7 . 7 29 . 7 ( 2 . 1 ) 6 . 0 ( ) 2 . 0 ( x 3 2 1 = + × + × - = = - × + × - = = - + × + × - = 1264 . 7 12 / )) 6402 . 1 ( 5 80 ( 2 . 1 ) 4685 . 8 ( ) 2 . 0 ( x 9385 . 4 8 / )) 6402 . 1 ( 6 45 ( 2 . 1 ) 6767 . 1 ( ) 2 . 0 ( x 6402 . 1 4 / ) 2 4685 . 8 6767 . 1 ( 2 . 1 ) 017 . 4 ( ) 2 . 0 ( x 3 2 1
Background image of page 4
Successive Over Relaxation Relaxation factor w (= )
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
» [A,b]=Example A = 4 -1 -1 6 8 0 -5 0 12 b = -2 45 80 » x0=[0 0 0]'
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 21

Lecture+27--Relaxation+method+_+Nonlinear+system -...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online