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soln_hw3 - MAT22B—1 HW 3 Problem I I Consider the...

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Unformatted text preview: MAT22B—1: HW 3 Problem I I. Consider the following first order ODE (a) Find the first order difference equation yn+1 = f (yn) that approximates this ODE using step size h = 0.1 (b) Suppose an initial value is yo is given, solve the difference equation in (a) in terms of the initial value yo. (c) Describe the behavior of the solution as n ——> 00. (a) E% Elder ’mebhool, ODE is C(WNDX lav ij'H‘31/l : ‘5jn-(‘GO 433 3 Di—Pfienflrsc/e 6?” using Hem/kg flea! (o at 3 MM WWW 0%” W "‘ O 3% fl (9 scum '60 outgmm a”? 03C 3Com gfifwt is t :Wf< l'f+:} m our case.) 33 :o,§ 4* ngCo 9% : 0.5"(L9¢~I2> +11! SCCJrOM 2‘; Zl a, r/‘Lg £0/ «1‘ i h" ”MW“ ’5' 7/”: (4+vZL)>/M*Lp. X, /.l 7,1 : L367 N A 22 " We ;, {My 5’ Y : //0§ ," y.g " 3357? 7.; : L232? >14, /.5”7/8” 7/0»! W W m 9., WW ,3 W w my” C, _ , 7,, — /./07£r 7.3 = (13??? ya .1: LZM’? 7"“, = Afr/7 Ajatm )‘usot y Lawr- ~/a.f fir a! 7k. / 4 , / 4 v finnfi. \ :c, It.» ,9 4 ./ 5"“‘2 '9 ¢=éi+cZ)/L 7L!) =/‘//017L 76.3) = /. ‘7’0/ 70:) :. pawn yo?) 5 /, (9/2? C/H‘riy 'ILLP‘i $13ggi3H2V“ m a» 1:.» a ,1 , ,7 m (:me w“ 7% 9b. 3 J y( I) : 3 : flaw 4. flag“ 7/116 538,5 )1.” H\ , 8&4; erh' ,1??? 743% L693}: Wtw‘ .573 ymw sew ydl): 'Izgy7 75:3): ”675‘? ~24 71M 65‘1‘54 Saflu'/:Dv\ {5 V: (érayf 4 3;.“4 ’55 2/; y(.;): ’ZQ'L/ 7&3)" .éLa’I ym) : two? fun: .7“)??? 7A6 VLU‘M’Y/ICA/ Sa)u)'lc?‘n—S arc jaw-HM) SM/l-K [/{r «a J r. (9M V‘er'w) J—a rf‘h fix/«Hf S 9 “34mm. 0 ‘ A m .4. J}, “/1, iw r. a AW S M ”W a w .310 «It i”. m 90 5 ¢ an,» a}, w in 2. + W f. 2 0,? > azw __ 0 ! 13V. 3 :r. W AW V M \ \W \ Euler approximation for 17 S ; 9:909:51 - mug?! I Spr’kjiffim (5 .M‘ 7? $0.! )1 _ 7 (9 0A7 I \ ’ 2‘ . SJ HOLD 0f! 51-45.; MAM N&¢}'LM§ )C"; {-3, Ogé'é‘, )LVWLA’j .15 fi Zg6'?Z 50 G’Le. It»: Hr‘c “fl a. ,7!) 3/” [‘5 7’ L12 5?» b» m n: Jae. a ’L 7‘11 nytJ a; WOM%L My '%L€M Y (W/m fig. 5:22 '1 u 7,712» Lax-M 554:. L»: m U 1* w _ _ ,, r 2 - ,5; 7/»: 2 <9 I: 5:]? ”f I'f ] I“ f / (*3 any! 2/0 ;, 3mm. )Zfié ”M’f‘j Y3! :0 'j’V‘CS 4L4 JCS/Arc] ,SVQI‘W’A'WM 34 7 Ji [7“ p93 3 PS LJ )4 r L!» IS 5 a? )wf 0/ far“ if) “we! pgchr 72% AF/flrolof'mtc Subgéeiuiaws P: 311 [59/7, // 7A€ Sazugrow 3:: [g/{VMJ.L&J it: 0/ L15. CM" [mt Use, (*5) ovum! Wk)4€ fa 5055*:4'u41ams, For #4“qu 0 7: . yen/S / £39”; ‘7’?» Anal a 4-0 Jul 0,? fi 229, 5°l/.Z.‘ EN“ 0 79mg “Wm”: NJ c ‘g‘wn/ m“ 11927577371. V!*-> M 7/ 7” _ ,J )+ L4 ,. nym ‘1’ 56;, RCQI/fimjgwj 3(I/t-5 d“ 6014 for Nine {wag-52g.“ n; ...
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