Numerical Computing

Overview

This course introduces numerical methods for approximating partial differential equations. Such methods are in widespread use today in engineering, in structural analysis, electromagnetics, fluid dynamics, thermodynamic analysis, and many other areas. Here we will deal with the simplest partial differential equations: parabolic equations (modelling unsteady heat diffusion), elliptic equations (steady-state heat diffusion) and hyperbolic equations (wave equation / unsteady convection).

In each case, we will consider the formulation of the PDE and the appropriate boundary conditions, and the construction of a suitable numerical approximation. We will analyse the accuracy and stability of the numerical method, and consider problems associated with the numerical solution procedure which often requires the solution of a large system of simultaneous linear equations.

Learning Outcomes

At the end of this course students will have an understanding and appreciation of the discrete approximation of continuous systems, and the computational methods required to solve the equations arising from such approximations