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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