Question

In: Advanced Math

use the method of order two to approximate the solution to the following initial value problem...

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

Expert Solution

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 .

Colby Messinger answered 2 years ago

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