Euler’s Method Exercises

Posted on March 13, 2015 by | 1 Comment

Hi everyone,

Here are some examples of Euler’s Method problems for you to try.  These are for practice only, they will not be collected.
NOTE: The first example is the one we solved in class on Thursday – I’m including it here for your reference.

Questions? Problems? Leave a comment on this post and I’ll respond here.

Example 1.  Given the initial value problem \frac{dy}{dt} = 3-2t-0.5y with y(0)=1, approximate the value of y(1).  Use 5 steps.

Example 2.  Consider y' = y \sin{t} -1.  Suppose y(0)=2.  What is y(3)?  Use a step size of h=0.5.

Example 3. If y'=\frac{x-4}{x-y+1}, use Euler’s method with 4 steps to approximate y(8) for the particular solution satisfying y(3)=3

Example 4.  Given \frac{dy}{dt}=e^\frac{t^2}{y^2+1} - y with y(-0.82)=0.97, estimate the value of y(1.28) using 6 steps.

Solutions to these examples are provided here for your reference – if you notice an error, please let me know by leaving a comment below (or sending an email).

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