# The effects of the choice of step size on the Euler's approximation

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?

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#### Solution Summary

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.

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