Introduction Notes Theory HOWTO Examples Engineering Error Questions Matlab Maple

Question 1

Given the IVP

y⁽¹⁾(t) = 1 - 0.25 y(t) + 0.2 t
y(0) = 1

approximate y(0.5), y(1), and y(1.5) using Euler's method.

Answer: 1.375, 1.750, 2.125.

Question 2

Given the same ODE as in Question 1, but with the initial condition y(1) = 2, approximate y(1.5) and y(2.0).

Answer: 2.35 and 2.7

Question 3

Given an IVP with an initial condition y(0) = y₀, if the second derivative is bounded by -8 < y⁽²⁾(t) < 8, on how large an interval can we estimate y(t) if we want to ensure that the error is less than 0.0001?

Answer: (-0.005, 0.005).

Topic 14.1: Euler's Method (Questions)

Question 1

Question 2

Question 3