Formula
1. Euler Rule
`y_1=y_0+hf(x_0,y_0)`
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Examples
1. Find y(0.2) for `y'=(x-y)/2`, y(0) = 1, with step length 0.1 using Euler method
Solution:
Given `y'=(x-y)/2, y(0)=1, h=0.1, y(0.2)=?`
Euler method
`y_1=y_0+hf(x_0,y_0)=1+(0.1)f(0,1)=1+(0.1)*(-0.5)=1+(-0.05)=0.95`
`y_2=y_1+hf(x_1,y_1)=0.95+(0.1)f(0.1,0.95)=0.95+(0.1)*(-0.425)=0.95+(-0.0425)=0.9075`
`:.y(0.2)=0.9075`
This material is intended as a summary. Use your textbook for detail explanation.
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