6.1. Numerical Methods for ODE’s#
In this section we will introduce the basic concepts required to solve time-dependent problems. As introduction, we focus on Ordinary Differential Equations (ODEs), that is, equations that only have derivatives with respect to time. We will later see how to extend these concepts to PDEs.
The introductory material will cover the following topics:
Introduction: introduction to the problem setting and notation.
Taylor Series: introduction to the concept of Taylor series to approximate functions.
ODE solvers: introduction to simple ODE solvers based on Taylor series.
Numerical error and stability: introduction to the concept of numerical error and stability.
Error control: introduction to adaptive time stepping techniques.