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H.W : Repeat size h=o.l and Compare with step the error with the Euler's methed,

H.W : Repeat size h=o.l and Compare with step the error with the Euler's methed,

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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EX s- Apply the improved Euler's method to the hzo-2, Xoz, Yo=o ý = x+ y ODE : Sol:- Ki = 0.2 (Xn +Yn) ( Xn ++ 2 Yn + ki) kz = 0. 2 to find Y,: k = c-2(0 to)=0 k2 = 012 (0+012 +o) = 0.04 Ź (0+ 0.04) to find y2: X1= Xo+h = 0.2, y, = o-02 KI=0:2 (X +4) = 0 -2 (0.2 +0.02) = 0.044 k2=0.2(Xi+0.2, Yh +ki) =0.2 (0.2+0.2 +0-0240. = 0,0928 = O = 0.0 2 92 = Y, + (• .044 +o.0928) = 0. 0884 Yn ki k2 Yexact Error o 0.0 0.0000 O.0000 G.0400 o. 0 200 O. 0000 O - 000 0 I 0.2 0 0200 0.0928 o.0884 0.0214 0.a440 e.0014 2 0.40.0884 0-0977 0.1572o.2158 0.0918 o.0034 3 0.6 0-2I580.1632 0.2358 . 41530. 2221 o.0063 40:8 0. 4153 O. 2431 O 33170-7027 0.4285 0.ol0 2 511.0 0.7027|0-34050.4487 1.0973 0:7183 o.0156 Compare the error with the Euler's method. Repent the error with the Euler's method. H.W: with step size h=o.l and ompare
Transcribed Image Text:EX s- Apply the improved Euler's method to the hzo-2, Xoz, Yo=o ý = x+ y ODE : Sol:- Ki = 0.2 (Xn +Yn) ( Xn ++ 2 Yn + ki) kz = 0. 2 to find Y,: k = c-2(0 to)=0 k2 = 012 (0+012 +o) = 0.04 Ź (0+ 0.04) to find y2: X1= Xo+h = 0.2, y, = o-02 KI=0:2 (X +4) = 0 -2 (0.2 +0.02) = 0.044 k2=0.2(Xi+0.2, Yh +ki) =0.2 (0.2+0.2 +0-0240. = 0,0928 = O = 0.0 2 92 = Y, + (• .044 +o.0928) = 0. 0884 Yn ki k2 Yexact Error o 0.0 0.0000 O.0000 G.0400 o. 0 200 O. 0000 O - 000 0 I 0.2 0 0200 0.0928 o.0884 0.0214 0.a440 e.0014 2 0.40.0884 0-0977 0.1572o.2158 0.0918 o.0034 3 0.6 0-2I580.1632 0.2358 . 41530. 2221 o.0063 40:8 0. 4153 O. 2431 O 33170-7027 0.4285 0.ol0 2 511.0 0.7027|0-34050.4487 1.0973 0:7183 o.0156 Compare the error with the Euler's method. Repent the error with the Euler's method. H.W: with step size h=o.l and ompare
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