For the sixth programming assignment of the semester we require tools which will assist us with the numerical solution of an IVP. Write functions which will implement the following methods:
See class notes for details concerning the implementation. Prepare a table of output values for each of the methods so they can easily be compared. If the values differ by more than a tolerance the stepsize may be too large. Search for optimal stepsize by doing several trials.
In the case of the Adams methods, investigate different "starter" methods and search for optimality.
Compare your results for a differential equation for which you know the solution, and for one for which the solution is unknown.
All sorts of things can be described using differential equations including traffic flow and space travel. After your experience so far, if you had to rely on one or more of these methods to "get home safely" which would you choose?