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ACM30140

Academic Year 2024/2025

Numerical Methods for PDEs (ACM30140)

Subject:
Applied & Computational Maths
College:
Science
School:
Mathematics & Statistics
Level:
3 (Degree)
Credits:
5
Module Coordinator:
Dr Chris Howland
Trimester:
Spring
Mode of Delivery:
On Campus
Internship Module:
No
How will I be graded?
Letter grades

Curricular information is subject to change.

This module introduces the methods and underlying theory used in the numerical solution of partial differential equations (PDEs). The finite difference method will be used to find solutions to evolutionary equations including the diffusion equation, advection equation, and wave equation. For each of these systems, the relative advantages/disadvantages of explicit and implicit numerical methods will be analysed by considering stability and convergence properties.
The module will end by discussing numerical solution of the Poisson equation in 2D, along with a brief overview of spectral methods for finding approximate solutions to PDEs.

About this Module

Learning Outcomes:

On completion of this module, students should be able to:
- Understand the meanings of order, stability and convergence in the context of numerical methods
- Use finite differences to construct systems of linear equations from a PDE
- Analyse iterative methods for the solution of systems of linear equations
- Use stability analysis to derive time step constraints on diffusive and advective PDEs
- Apply finite difference and spectral methods to solve PDEs in Python

Student Effort Hours:
Student Effort Type Hours
Autonomous Student Learning

72
Lectures

24
Tutorial

12
Total

108

Approaches to Teaching and Learning:
Lectures and tutorials.

Requirements, Exclusions and Recommendations
Learning Requirements:

The prerequisites for ACM30140 are:
- a course in PDEs
- knowledge of coding in Python with Jupyter notebook
- knowledge of linux commands, and using the terminal to connect to servers.


Module Requisites and Incompatibles
Not applicable to this module.
 

Assessment Strategy
Description Timing Component Scale Must Pass Component % of Final Grade In Module Component Repeat Offered
Assignment(Including Essay): Computational take-home assignment Week 9, Week 10 Alternative linear conversion grade scale 40% No
15
 No
Assignment(Including Essay): 6 Brightspace quizzes Week 1, Week 2, Week 3, Week 4, Week 5, Week 6, Week 7, Week 8, Week 9, Week 10, Week 11, Week 12 Alternative linear conversion grade scale 40% No
15
 No
Exam (In-person): Class test Week 6, Week 7 Alternative linear conversion grade scale 40% No
20
 No
Exam (In-person): End Of Semester Exam End of trimester
Duration:
2 hr(s)
 Alternative linear conversion grade scale 40% No
50
 No

Carry forward of passed components
No
 

Resit In Terminal Exam
Autumn Yes - 2 Hour
Please see Student Jargon Buster for more information about remediation types and timing. 

Feedback Strategy/Strategies

• Feedback individually to students, post-assessment
• Group/class feedback, post-assessment
• Online automated feedback

How will my Feedback be Delivered?

Not yet recorded.

A. Iserles, A First Course in the Numerical Analysis of Differential Equations, 2nd ed. Cambridge: Cambridge University Press, 2008.
E. Süli and D. F. Mayers, An Introduction to Numerical Analysis. Cambridge: Cambridge University Press, 2003.

Timetabling information is displayed only for guidance purposes, relates to the current Academic Year only and is subject to change.
Spring Lecture Offering 1 Week(s) - 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33 Fri 16:00 - 16:50
Spring Lecture Offering 1 Week(s) - 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33 Mon 15:00 - 15:50
Spring Tutorial Offering 1 Week(s) - 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33 Tues 16:00 - 16:50
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