Explore BrainMass
Share

Explore BrainMass

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

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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?

    © BrainMass Inc. brainmass.com October 9, 2019, 4:16 pm ad1c9bdddf
    https://brainmass.com/math/numerical-analysis/27440

    Attachments

    Solution Preview

    Hi there!
    Here is the solution to this problem.
    I also attached the Excel file that I used to show the ...

    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.

    $2.19