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Example: solve y'=ty+1, yo = y(0) = 1, 0

Example: solve y'=ty+1, yo = y(0) = 1, 0

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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t1=0.25 t2=0.5 t3=0.75 t4=1
Example: solve y'=ty+1, yo = y(0) = 1, 0<t<1, h=0.25 Solution: fis linear in y. So, solving the problem using modified Euler method for y, yields h Yn = Yn-1 +(y'n-i+y',) п-1 h = yn-1 + (t,-1Yn-1+1+t„y„+1) 2 ə Y„(1--t,) = y,„-1(1+÷t,1)+h h (1+ t,-1). Yn =- h Yn-1 + h (1 - 11
Transcribed Image Text:Example: solve y'=ty+1, yo = y(0) = 1, 0<t<1, h=0.25 Solution: fis linear in y. So, solving the problem using modified Euler method for y, yields h Yn = Yn-1 +(y'n-i+y',) п-1 h = yn-1 + (t,-1Yn-1+1+t„y„+1) 2 ə Y„(1--t,) = y,„-1(1+÷t,1)+h h (1+ t,-1). Yn =- h Yn-1 + h (1 - 11
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