Question

An initial-value problem is given by the differential equation,

f(x,y) = x + y, y(0) = 1.64

The Euler-midpoint method is used to find an approximate value to y(0.1) with a step size of h = 0.1.

Then use the integrating factor method, to find the exact value of y(0.1).

Hence, determine the global error, giving your answer to 5 decimal places.

Note that Global Error = Approximate Value - Exact Value.

Answer 1

after calculating the y' and y'' values.

the values come up be 2.7731947639

which when rounded to 5 decimal places gives the answer as: 2.773195

Answer 2

after re-calculating the euler-midpoint method. the value I got was 1.8172 while using normal euler method is 1.968.

however, I can't seem to find the exact solution to minus off the 1.8172 value to get the global error.