Numerical Solutions

Abstract

In general, nonlinear ordinary differential equation models do not have solutions that can be written down explicitly. Instead, solutions to these equations must be approximated numerically. This chapter reviews two classes of numerical methods: Euler and Runge–Kutta methods that solve equations forwards in time starting from an initial value, and collocation methods which approximate solutions using a basis expansion. The chapter also discusses when these methods can break down and ways to transform a differential equation to improve their performance.