Lecture 8-9 | Errors | Advanced Mathematical Methods for Engineers

Overview
In this module you will learn how to solve Ordinary Differential Equations (ODEs) both using analytical and numerical methods. Many engineering processes are described by either a single ODE or system of ODEs. Examples include vibrations in systems, spreading of pathogens, or chemical reaction mechanisms. You will learn how to code numerical methods to solve ODEs, solve systems of ODEs, and how to make sure that the numerical solution of ODEs is accurate, even in cases where no analytical solutions are known.

Learning Objectives
By the end of this module, you will be able to:

8.1 - Solve an ODE using explicit/ implicit/ modified/ midpoint Euler method using self-coded functions.
8.2 - Solve an ODE using Runge-Kutta methods using self-coded functions.
8.3 - Identify errors of ODE solution methods and their formal order.
8.4 - Solve higher-order ODEs and system of ODEs using self-coded functions.
8.5 - Identify numerical solution methods for stiff ODEs.

Lecture Videos:
Lecture 8.1: ODEs Overview
Lecture 8.2: Analytical Solutions of ODEs
Lecture 8.3: Numerical Solutions of ODEs
Lecture 8.4: Euler's Explicit Method
Lecture 8.5: Euler's Implicit Method
Lecture 8.6: Stability
Lecture 8.7: Modified Euler Method
Lecture 8.8: Midpoint Euler Method
Lecture 8.9: Errors
Lecture 8.10: Runge-Kutta Methods
Lecture 8.11: Accuracy of Numerical Solutions of ODEs
Lecture 8.12: Numerical Solutions of Systems of ODEs
Lecture 8.13: Numerical Solutions of Higher Order ODEs
Lecture 8.14: Stiff ODEs