Description
Computer Assisted Questions:
5. Consider the IVP y
0 = 3y + 3t, y(0) = 1 (solution y(t) = 4
3
e
3t − t − 1/3).
a) Approximate y(1) using Euler’s Method with h = 1, 0.1, and 0.01. Compute the relative
error for each approximation.
b) Approximate y(1) using Heun’s Method with h = 1, 0.1, and 0.01. Compute the relative
error for each approximation.
c) Approximate y(1) using Runga-Kutta’s 4-step Method with h = 1, 0.1, and 0.01. Compute
the relative error for each approximation.
6. Consider the IVP y
0 = −ty, y(0) = 1 (solution y(t) = e
−t
2/2
).
a) Approximate y(1) using Euler’s Method with h = 1, 0.1, and 0.01. Compute the relative
error for each approximation.
b) Approximate y(1) using Heun’s Method with h = 1, 0.1, and 0.01. Compute the relative
error for each approximation.
c) Approximate y(1) using Runga-Kutta’s 4-step Method with h = 1, 0.1, and 0.01. Compute
the relative error for each approximation.
7. Consider the IVP y
0 = t
2 − y, y(0) = 1 (solution y(t) = −e
−t + t
2 − 2t + 2) – see question 4.
a) Approximate y(1) using a 2nd and 3rd order Taylor Series Method with h = 1. Compute
the relative error for each approximation.