Module Information

Module Identifier
Module Title
Advanced Numerical Methods
Academic Year
Semester 1
PH26620 or equivalent
Other Staff

Course Delivery



Due to Covid-19 students should refer to the module Blackboard pages for assessment details

Assessment Type Assessment length / details Proportion
Semester Assessment Written Report  50%
Semester Assessment Essay  30%
Semester Assessment Numerical Exercises  20%
Supplementary Assessment As determined by the Departmental Exam Board  100%

Learning Outcomes

On successful completion of this module students should be able to:

1. Formulate numerical solutions to mathematical and physical problems.
2. Utilise various techniques for scientific computing and analysis.
3. Formulate and evaluate numerical programs that implement the relevant algorithms.
4. Apply methods of solving large systems of simultaneous equations.
5. Utilise Monte Carlo methods to solve problems in statistical mechanics.
6. Compose a written report on the applied techniques and their results.


Numerical solutions to mathematical and physics problems is a cornerstone of both physics and applied mathematics research. This module is a continuation of the practical-based module PH36010. The numerical techniques are more advanced and will require more detailed understanding of the numerical methods.

Brief description

This module builds on the Numerical Methods module PH36010. Methods of solving (large) systems of simultaneous linear equations are introduced. This is then used to numerically solve partial differential equations. Monte Carlo methods are introduced as a general method. More specifically, Metropolis Monte Carlo methods for solving problems in statistical mechanics are covered. The students will implement these algorithms and apply them to simple physical problems.


LU decomposition.
Iterative methods for solving sparse systems of linear equations.
Numerical methods for partial differential equations.
Monte Carlo methods.
Metropolis Monte Carlo methods for simulation of statistical mechanical systems.

Module Skills

Skills Type Skills details
Application of Number Throughout the module.
Communication Writing reports.
Information Technology This module involves programming and computational visualisation.
Personal Development and Career planning Programming skills.
Problem solving Throughout the module.
Subject Specific Skills Programming, numerical methods.


This module is at CQFW Level 7