Computational Partial Differential Equations with Applications

Module code: MA7011

The mathematical models arising from countless physical and natural phenomena as well as social sciences such as economics and finance are based on Partial Differential Equations (PDEs). The solution of PDE problems of practical importance is rarely available in closed form, hence the need for computational methods able to deliver accurate and reliable numerical (approximate) solutions.

This module provides the mathematical foundation as well as practical implementation knowledge of computational schemes for PDEs, using Finite Differences (FD). You will learn fundamental properties of numerical methods (consistency, stability, convergence) and how to use these notions to select the right method depending on the type of PDE problem that needs to be solved.  You will learn how to implement and analyse FDs for some important applications including nonlinear problems and obstacle problems relevant to physical and financial modelling.