Beyond Euler's Method: Implicit Finite Differences in an Introductory ODE Course

Abstract

A typical introductory course in ordinary differential equations (ODEs) exposes students to exact solution methods. However, many differential equations must be approximated with numerical methods. Textbooks commonly include explicit methods such as Euler's and Improved Euler's. Implicit methods are typically introduced in more advanced courses and texts aimed specifically at numerical analysis or partial differential equations. This article will present techniques and advantages of using implicit methods in an early ODE course.