Many students are challenged to understand the nature of Big Oh in relating it to the order of accuracy of numerical methods. In this exercise, we are using the central divided difference approximation of the first derivative of the function to ease some of the mystery surrounding the Big Oh.
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In this example, we are given an ordinary differential equation and we use the Taylor polynomial to approximately solve the ODE for the value of the dependent variable at a particular value of the independent variable. As a homework assignment, do the following.
1) compare the approximate solution with the exact one, and
2) get another approximate solution by using a third order Taylor polynomial.
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