Examples

  1. Suppose that you are using Euler's method and you estimate that your solution at a certain time point f(t29) is "".

    How much would you have to reduce the time step h in the solution algorithm to reduce the error at this point to "" ?

    You would reduce it by 100x because Euler's method is a first order method.

  2. Suppose that you are using a second order method and you wish to reduce the error in your solution from 10-3 to 10-5.

    How much would you have to reduce the time step h?

    You would reduce h by 10x because a second order method reduces error such that "" .