Explore BrainMass
Share

Explore BrainMass

    Euler and Modified Euler's method

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

    I need help using Euler an the improved Euler methods: (look at attachment for better formula display)

    1. Consider the initial value problem y' = 2xy, y(1) = 1. Use the Euler's method and improved Euler's method with h = 0.1and h = 0.05 to obtain approximate values of the solution at x = 1.5. At each step compare the approximate value with the actual value of the analytic solution. Also calculate the bound for the local truncation error using the formula: (look at attachment)

    2. Consider the initial value problem ' ( 1) , (0) 2. 2 y = x + y − y = Use the improved Euler's method with h = 0.1and h = 0.05 to obtain approximate values of the solution at x = 0.5. At each step compare the approximate value with the actual value of the analytic solution.

    © BrainMass Inc. brainmass.com October 10, 2019, 7:12 am ad1c9bdddf
    https://brainmass.com/math/computing-values-of-functions/euler-modified-eulers-method-572174

    Attachments

    Solution Preview

    Hello and thank you for posting your question to Brainmass.

    The solution is attached below in two files. the files ...

    Solution Summary

    The solution shows how to approximate the result of a first order ordinary differential equation using Euler's method and the modified Euler's method.

    $2.19