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Use Euler's method to approximate y(1.9). Start with step size h=0.1, and then use successively smaller step sizes (h = 0.01, 0.001, 0.0001, etc.) until successive approximate solution values at x= 1.9 agree rounded off to two decimal places. y' =x? +y? - 2, y(0)= 0

Use Euler's method to approximate y(1.9). Start with step size h=0.1, and then use successively smaller step sizes (h = 0.01, 0.001, 0.0001, etc.) until successive approximate solution values at x= 1.9 agree rounded off to two decimal places. y' =x? +y? - 2, y(0)= 0

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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Use Euler's method to approximate y(1.9). Start with step size h = 0.1, and then use successively smaller step sizes (h = 0.01, 0.001, 0.0001, etc.) until successive approximate solution values at x = 1.9 agree rounded off to two decimal places. y' =x? +y? - 2, y(0) = 0 The approximate solution values at x = 1.9 begin to agree rounded off to two decimal places between h= 0.001 andh= 0.0001. So, a good approximation of y(1.9) is 0.11.
Transcribed Image Text:Use Euler's method to approximate y(1.9). Start with step size h = 0.1, and then use successively smaller step sizes (h = 0.01, 0.001, 0.0001, etc.) until successive approximate solution values at x = 1.9 agree rounded off to two decimal places. y' =x? +y? - 2, y(0) = 0 The approximate solution values at x = 1.9 begin to agree rounded off to two decimal places between h= 0.001 andh= 0.0001. So, a good approximation of y(1.9) is 0.11.
Expert Solution
Step 1

 

Euler's Method:

Let the initial value problem is given as

y'=f(x,y) ,  y(x0)=y0.

Then the iteration formula is given by

yn+1=yn+h f(xn,yn)

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