4. Consider the initial value problem (IVP): y'(t) = 3+t+y 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?
Here is the solution to this problem.
I also attached the Excel file that I used to show the ...
The Euler's method is a first order numerical method to solve initial value problems. This solution shows how to implement the Euler's method and how the step size choice effects the error in the approximation.