Lecture 9-5 | Accuracy of Numerical PDE Solutions | Advanced Mathematical Methods for Engineers

Overview
In this module, you will learn how to solve Partial Differential Equations (PDEs) using analytical and numerical methods. Almost all engineering processes can be described by a PDE or system of PDEs. Examples include fluid dynamics, high-speed aerodynamics, heat transfer, combustion processes, and fracture dynamics.

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

9.1 - Revert PDEs to systems of ODEs by applying finite differences.
9.2 - Solve a PDE numerically with finite differences and Runge-Kutta methods using self-coded functions.
9.3 - Identify the formal order of accuracy of a PDE solution method.

The included lectures in this module are:
Lecture 9.1: Overview of PDEs
Lecture 9.2: Analytical Solutions PDEs
Lecture 9.3: Numerical Methods
Lecture 9.4: Coding Numerical Methods for PDEs
Lecture 9.5: Accuracy of Numerical PDE Solutions
Lecture 9.6: Numerical Methods for PDEs in 2+D