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Lecture 9-6 | Numerical Methods for PDEs in 2+D | 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