# Euler and Modified Euler's method

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 âˆ’ 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.

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

Hello and thank you for posting your question to Brainmass.

The solution is attached below in two files. the files are identical in content, only differ in format. The first is in MS Word format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.

In addition, there is an excel file with the actual calculation tables. Graphs were done by MAPLE

Feedback is always appreciated.

I hope this helps

Thanks again

Yinon

https://brainmass.com/math/computing-values-of-functions/euler-modified-eulers-method-572174