MA4NSP-Numerical Solution of Partial Differential Equations

Module Provider: Mathematics and Statistics
Number of credits: 10 [5 ECTS credits]
Level:7
Terms in which taught: Spring term module
Pre-requisites: MA2NAN Numerical Analysis and MA3NAT Numerical Analysis II
Non-modular pre-requisites:
Co-requisites:
Modules excluded:
Current from: 2019/0

Module Convenor: Dr Tristan Pryer

Email: t.pryer@reading.ac.uk

Type of module:

Summary module description:
This module covers numerical methods for solving partial differential equations.

Aims:
To derive, implement and analyse numerical methods for partial differential equations.

Assessable learning outcomes:

By the end of the module, students are expected to be able to:

• Formulate and implement numerical methods for partial differential equations of hyperbolic, elliptic and parabolic type, and to analyse stability, consistency and convergence properties of these schemes;

Additional outcomes:

Students will be expected to be able to have some understanding of:

• Classification of partial differential equations into hyperbolic, elliptic and parabolic types
  
• Classical, weak and variational formulations;
  
• The limitations of certain numerical methods, and how these can potentially be rectified by alternative approaches;
  
• basic issues relating to the solution of the resulting systems of linear equations;
  
• The principles of error estimation.

In addition, students will reinforce their basic programming skills. 

Outline content:

Partial differential equations can be used to model many physical systems. Construction of analytical solutions is impractical for all but the most basic scenarios, hence in practice, numerical methods must be developed for their solution. In order to have confidence in any chosen numerical scheme, it is important to be able to derive bounds on the error. In this module, we derive, implement and analyse numerical methods for the solution of model partial differential equations, establishing a basic framework for the analysis of more general problems. 

Brief description of teaching and learning methods:

The material will be a reading course, supported by formative problem sheets and assignments.  

Contact hours:

	Autumn	Spring	Summer
Seminars		10
Guided independent study:		90
Total hours by term	0	100	0
Total hours for module	100

Summative Assessment Methods:

Method	Percentage
Written assignment including essay	50
Oral assessment and presentation	50

Summative assessment- Examinations:

Summative assessment- Coursework and in-class tests:

Written report(s) in latex complete with appended code and an oral assessment.

Formative assessment methods:
Problem sheets.

Penalties for late submission:
The Module Convener will apply the following penalties for work submitted late:

where the piece of work is submitted after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for that piece of work will be deducted from the mark for each working day[1] (or part thereof) following the deadline up to a total of five working days;

where the piece of work is submitted more than five working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.

The University policy statement on penalties for late submission can be found at: http://www.reading.ac.uk/web/FILES/qualitysupport/penaltiesforlatesubmission.pdf
You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Assessment requirements for a pass:

At least 50% overall. 

Reassessment arrangements:

Resubmission of the report(s) and a repeat oral assessment in August/September 

Additional Costs (specified where applicable):
1) Required text books:
2) Specialist equipment or materials:
3) Specialist clothing, footwear or headgear:
4) Printing and binding:
5) Computers and devices with a particular specification:
6) Travel, accommodation and subsistence:

Last updated: 11 April 2019