Euler's Method

 

This is just a posting of one of the examples done at Group. I tried to color code where the numbers go, but you might need to refer to your notes for more details.

Given: y' = y + t , y(0) = 1, Dt = .1

Find y(.5)

 

y' = y + t , y(0) = 1, Dt = .1

New = Old + Change

y(.1) = y(0) + [y'(0) Dt]

y(.1) = 1 + [ (y+t) (.1)]

y(.1) = 1 + [ (1+0) (.1)]

y(.1) = 1 + .1

y(.1) = 1.1

y(.1) = 1.1

New = Old + Change

y(.2) = y(.1) + y'(.1) Dt

y(.2) = 1.1 + (1.1+.1) (.1)

y(.2) = 1.1 +.12

y(.2) = 1.22

y(.2) = 1.22

New = Old + Change

y(.3) = y(.2) + y'(.2) Dt

y(.3) = 1.22 + (1.22+.2) (.1)

y(.3) = 1.22 +.142

y(.3) = 1.362

New = Old + Change

y(.4) = y(.3) + y'(.3) Dt

y(.4) = 1.362 + (1.362+.3) (.1)

y(.4) = 1.362 +.1662

y(.4) = 1.5282

New = Old + Change

y(.5) = y(.4) + y'(.4) Dt

y(.5) = 1.5282 + (1.5282+.4) (.1)

y(.5) = 1.5282 +.19282

y(.5) = 1.72102

 

 By

Lee DeAnda

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