Unit 1: Numerical Integration of Ordinary Differential Equations

Contents of a Unit

Each unit is composed of:

  • a set of readings that include some short videos to emphasize key ideas. Throughout the readings are embedded questions that are intended to help check your understanding of the material in the readings and videos. Each embedded question also has a corresponding solution, which you may use to check you answer.
  • sample problems that are similar to the homework problems. A solution is provided for each sample problem. The sample problems do not have answers to be entered, but we suggest you attempt to solve the sample problems before continuing.

1.1 Overview

1.2 Discretizing ODEs

1.3 Order of Accuracy

1.4 Convergence

1.5 Zero Stability and the Dahlquist Equivalence Theorem

1.6 Systems of ODE's and Eigenvalue Stability

1.7 Stiffness and Implicit Methods

1.8 Multi-Step Methods

1.9 Runge-Kutta Methods