In: Advanced Math
use the method of order two to approximate the solution to the following initial value problem y'=e^(t-y),0<=t<=1, y(0)=1, with h=0.5
Solution: Given Initial value problem is
with h=0.5.
Let
The Taylor's method of order two for general initial value problem (*) is given by
where h is small.
Therefore,The Taylor's method of order two for general initial value problem (i) is given by
With , equation (**) becomes
Therefore, with , we have
Therefore and .