Use the Euler method?

Question

Use the Euler method with h=0.05 to find approximate values of y'=3+t-y, y(0)=1 at t=0.1, 0.2, 0.3, and 0.4.

 

Answer: 1.1975, 1.38549, 1.56491, 1.73658

Answer 1

Euler's method:

 

y_n+1=y_n+h y'(t_n,y_n)

 

In your case:

 

y_n+1=y_n+ 0.05 (3+t_n-y_n)

 

Therefore,

 

y₁=y(0.05)=1+ 0.05(3+0-1) =1.1

y₂=y(0.10)=1.1+0.05(3+0.05-1.1) = 1.1975

etc.

 

It's easiest to use a programming language to code up this method with a recursive loop.

Answer 2

y(n+1) = y'(n)h + y(n), where y'(n) = 3+t(n)-y(n)

y(0) = 1

y(0.05) = 1.1

y(0.1) = 1.1975

...

y(0.2) = 1.38549375

 

...

y(0.3) = 1.564988109

...

y(0.4) = 1.736579569