COT - December 8

# COT - December 8 - December 8, 2009 Error ∅ Δt 2 Δt 3...

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: December 8, 2009 Error ∅ Δt 2 Δt 3 Δt 4 Method Explicit & Implicit Euler 2nd order RK 4th order RK December 8, 2009 x=f(t)Ralston has error Δt 4 “Classical” 4th order RK xt+∆t=xt+∆tΦ Φ=16k1+13k2+13k3+16kn k1=f(xt,t) k2=f(xt+12∆tk1, t+∆t2) k3=f(xt+12∆tk2, t+∆t2) k4=f(xt+∆tk3, t+∆t) ***Go to programming xcel file for code Example 1 x1+2x1x2+sinx2x1=0 x2+2x1+x2x2+cosx1x2=0 I.C. x10=4 x20=3 x10=7 x20=5 New variables y1=x1 y2=x2 y3=x1↔y3=y1 y4=x2↔y4=y2 y3+2y3y2+siny2y1=0 y4+2y2y3+2y2y4+cosy1y2=0 December 8, 2009 Example 2 x1+2x1x2+sinx2x1=0 x2+2x2x1+x2x2+cosx1x2=0 I.C. x10=4 x20=3 x10=7 x20=5 New variables y1=x1 y2=x2 y3=x1↔y3=y1 y4=x2↔y4=y2 f=y3+2y3y2+siny2y1=0→y3-2y3y2-siny2y1 f=y4+2y2y3+2y2y4+cosy1y2=0→y4+2y2y3=-y2y4-cosy1y2 102y21y3y4=-2y3y2-siny2y1-2y2y4-cosy1y2 2y2y4-cosy1y2 → y3y4=10-2y21-2y3y2-siny2y1- December 8, 2009 Exam 2004 #1 x+3x+2=0 x0=0 x0=0 Part a y1=x y2=x→y1=y2 →y2+3y2+2=0 →y2=-3y2-2 y1=y2 y1=y2 y2=-3y2-2 y=010-3y1y2+0-2 A=010-3 b=0-2 y0=y1(0)y2(0)=x(0)x(0)= 00 λ1=0λ3=-3 w1:0-(0)103-(0)w11w21= 00= w21=0-3w21=0w11=C→w1=10 w2:0-(-3)10-3-(-3)w12w22= 0→ Σw12+w22=00=0w12=Cw22=-3C→w2=1-3 W=1103 W-1=1-3-3-101=11/30-1/3 ξt=W-1b=11/30-1/30-2=-2/32/3 z0=W-1x0=11/30-1/300=00 z1t=zi0eλit-ξiλi1-eλit=0-(-23)01-1→z1t=-23t z2t=0+(2/3)-31-e-3t=291-e-3t REVIEW SESSION ON TUESDAY AT 4PM ...
View Full Document

## This note was uploaded on 01/08/2010 for the course COT 3502 taught by Professor Hawkins during the Fall '08 term at University of Florida.

Ask a homework question - tutors are online