EX s- Apply the improveed Euler's method to the ý = x+y , hzo-2, Xozo, Yo=o ODE : Sol:- K = 0.2 (Xn +Yn) K2 = 0:2 (Xn+o.2 to find ,: + Yn + ki) k = 0-2(0 +o) =0 k2 = 012 (0+012 + o) = 0.04 글 (0+0.04) = 0.02 = O to find y2: X1= Xe+h = 0.2 y, = 0-02 KI=0:2 (x, +4) = 0 -2 (o.2 +0.02) k2=0.2(X1+0.2, +k) =0.2 (0.2+0.2 +0-0240 = 0,0928 = 0.044 Y2 = Y, + (0 .044 +o.0928) = . 0884 %3D in Yn ki K2 Yexact Error o 0.0 0.0000 O. 0000 O.0400 0.0200 O. 0000 O. 000 0 O.0200 0.a440 0.0928 0.0884 0.0214 0.0014 2 040.0884 0.0977 0.1572 o.2158 0.0918 O.0034 3 0.6 0.2158 0.1632 0-2358 .41530.2221 o.0063 4|018|0.니153 O. 2431 O 33170-7027 0.4285 o.ol0 2 511.0 |0.구02구|0.340S |e.4487 1.0973 0.7183 o.0156 Compare the error with the Euler's method. H.w: Repeat with the error with the Eulers method. size h=o.l and ompare step
EX s- Apply the improveed Euler's method to the ý = x+y , hzo-2, Xozo, Yo=o ODE : Sol:- K = 0.2 (Xn +Yn) K2 = 0:2 (Xn+o.2 to find ,: + Yn + ki) k = 0-2(0 +o) =0 k2 = 012 (0+012 + o) = 0.04 글 (0+0.04) = 0.02 = O to find y2: X1= Xe+h = 0.2 y, = 0-02 KI=0:2 (x, +4) = 0 -2 (o.2 +0.02) k2=0.2(X1+0.2, +k) =0.2 (0.2+0.2 +0-0240 = 0,0928 = 0.044 Y2 = Y, + (0 .044 +o.0928) = . 0884 %3D in Yn ki K2 Yexact Error o 0.0 0.0000 O. 0000 O.0400 0.0200 O. 0000 O. 000 0 O.0200 0.a440 0.0928 0.0884 0.0214 0.0014 2 040.0884 0.0977 0.1572 o.2158 0.0918 O.0034 3 0.6 0.2158 0.1632 0-2358 .41530.2221 o.0063 4|018|0.니153 O. 2431 O 33170-7027 0.4285 o.ol0 2 511.0 |0.구02구|0.340S |e.4487 1.0973 0.7183 o.0156 Compare the error with the Euler's method. H.w: Repeat with the error with the Eulers method. size h=o.l and ompare step
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:EX s- Apply the improved Euler's method to the
ý = x+y
ODE :
hzo-2, Xoz, Yo=o
Sol:- Ki = 0.2 (Xn +Yn)
( Xn ++ 2
Yn + ki)
k2 = 0. 2
to find Y,:
k = 0-2(0 to) =0
k2 = 012 (0+0:2 +o) = 0.04
Ź (0+ 0.04)
to find y2: X1= X. +h = 0.2, Y, = 0-02
KI=0:2 (X, +4) = 0 -2 (0.2 +0.02) = 0.044
k2=0.2(Xi+0.2, Yi +ki) =0,2(o.2+ 0.2 +0-024 0.
= 0,0928
= O
= 0-0 2
Y2 = Y, + (• .44 +o.0928) = e.0884
Yn
ki
K2
Yexact
Error
o 0.0 0.0000
O. 0000
G.0400 0.0200
O. 0000
O - 000 0
I 0.2 0 0200
0.0928 o.0884 0.0214
2 0.40.0884 0-0977 0.1572o.2158 0.0918
0.0440
G.0014
o.0034
3 0.6 0.2158 0.1632
0.2358 . 41530. 2221
o.0063
4 0:8 0. 4153
O. 2431
O 33170-7027 0.4285 0.ol0 2
51.00.7027|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:
size h=o.l and Compare
with
step
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