ABSTRACT
Numerical techniques are one way to determine approximate (and in many cases very good) solutions to a differential equation. In this chapter Euler's method is developed from locally linear approximation (tangent line solutions) given an initial value problem, and then extended to systems of differential equations. The tradeoffs between step size of the numerical method and computational time are introduced to gauge timing of the numerical method. The process of using Euler's method (or the associated Runge-Kutta method) is a workflow in R (Approximate → Forecast → Repeat) using associated functions in the demodelr package.
