Lecture 9-2 | Analytical Solutions PDEs | Advanced Mathematical Methods for Engineers
Автор: Jonas' Class Notes
Загружено: 2024-02-25
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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
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