Taylor polynomial is an essential concept in understanding numerical methods. Examples abound and include finding accuracy of divided difference approximation of derivatives and forming the basis for Romberg method of numerical integration.
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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