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Chapter3Qualitative and Numerical Methods of Approximation

This chapter will introduce two methods of approximating solutions to first order DEs. The first method is qualitative, which means that it allows us to understand the behavior of solutions. This qualitative method is quick and easy, but it does not yield any real data, i.e. points that can be plotted. The second method, numerical simulation, yields a lot of plottable data, but it also requires more effort. There are actually many different numerical methods and these are classified by their order.

  • Qualitative: phase diagrams

  • Numerical:

    1. Euler's Method (1st order)

    2. Heun's Method (2nd order)

    3. Runge Kutta Method (4th order)