Assignment:
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?
Provide complete and step by step solution for the question and show calculations and use formulas.