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Question 2 4 pts a) Find the upper bound for the local truncation error if you solve the equation with the explicit Euler's method b) Find the upper bound for the global error as a function of t and h if you solve the equation with the explicit Euler's method y = 3 sin(2y) y (0) = 1, 0<t<} HTML Editores

dont use matlab

yes

Answer 1

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o< t <1 - [t, 38 x 42 Z al y'= 3 Sim (2y), y lo) = 4, roflt, y(t) = 3 sin(2y(t)), bet he be the stepsize Euler in method: Inte=Ynth fltn, Yn), hat hati - th 3 y'etle 11t, y141) - 3 sin(2y cel) - y" (t)= $+ [+, 91+1] + ty y (+) y' lt) 3 as (2414) y'lt) to ly"(t) | <31 uszy llylle) <3X1 X3 | Simay | 9" (0) < 9 M = mare (y" lt)) = 9 to Translation Error En Is M h² = 1 En l = 4.5h2 An upper bound for local truncational Error = 4. (6) Global truncation Error En = y(tn) yn no Enlem lekt_ 1) h - (L) where M = max llot ++ by lt, y) l , k = max Itylt, o) 1 (t,y) ER 6+ = 0, y = 3 cus(2 y (4) ) * 2y'1t) do 16+ + F by < 3 x 6 x 3 = 54 so M=54 löylt,y) 13 6x3 = 10 SA (e - 1) h 2x38 = Enl < 1.5 h L ) Am upper bound for Global T. E. -4.56? 2 k t, JER f so k=18 18t so l Enla 3 18 t e 1.5 holes e18 ta