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quiz 4(1) - 640-244 Quiz 4 NAME SECTION(1 Use Euler’s...

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Unformatted text preview: 640-244 Quiz 4 NAME: SECTION: (1) Use Euler’s method to find an approximate value of y(0.2) with step size At = 0.1, where y(t) is the solution of the initial value problem d =/ —y=3+t—y yo dt {3:0 €,:o.l y(0) = 1- What is the order of the global error if we use Euler’s method? What is the order of the global error if we use the improved Euler’s method? What is the order of the global error if we use the Runge—Kutta method? 3,: f{+o,%,)4t +3. #2; ’C/‘v:g,)(°.l3 , 9’ Order. 075 glob“! 8,,” f(3+o«.)(o,,) * ’ g 5+on-l.1)(o.o+ L2 Ed” 4“ = 0.! ; fix” a ("00 (0.1) +1.2 Errand Em" (150‘: o. 0/ ['2 = z: 0.19 ”'2. my e‘Kan, (40",: 0.0001, . 51,18 3&11). 2 qu (2) Determine the longest interval in which the initial value problem (a: — 2)y” + y’ + (x — 2)(tan x)y : 0 y(3) : 17 y’(3) = 2 is certain to have a unique solution. R91») fr‘i‘Q, Jll? 36%;,oy‘ 6L3 y” * (X'Z) ‘& I I- 6"“) 3‘0 , s ' funk ‘ . g '5 Undefined or,“ /\'= -77/ rt 3 y‘ i 5 "‘1 2; l/Z) ”/2, ”IE, . +2 '5 “MP/meal m‘ ng Fossils: I"*"W ’5 i n.) (Wan/2), (fl/2,2), (2 37772)) {37% 9%) «H—efl—it—N~ : . ' ’ ._ t, ' +° 3 5 ”‘ {'21 g1V2) , 30 We. hon/g ck umW¢ l" _ ll: l 31 SIT \ a ‘ , z /z "‘ “in; A S‘o/K’hon on (2, “Ir/2). ...
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