Example 3.  Plot the error for Euler's method and the modified Euler's method.

Solution 3.

Just for fun, compare the error for the Euler and modified Euler solutions.

Since we have the analytic or "true solution" at hand, we can run experiments to verify that Euler's method has order  ,  and   the Modified Euler's method has order  .   Reduce the step size by   and see what happens to the error.

(c) John H. Mathews 2004