The effects of the choice of step size on the Euler's approximation
Solve the following problem:
1. Consider the initial value problem (IVP): y'(t) = 3+t-y subject to y(0)=1
a) Approximate y(1) using Euler's method and step sizes of 0.2. Perform these calculations by hand. What is the exact value of y(1)?
b) Use the computer (e.g. ODE Architect, ODE Toolkit, or your own program) to approximate y(1) using step sizes of 0.1, 0.05, 0.025 and 0.01. What is the general relationship between the error of the approximation and the step size?