What will I learn on this module?
You will learn the various numerical techniques used to solve partial differential equations (PDEs). PDEs are widely used to describe phenomena in the natural world as well as in cultured and manufactured reality. These powerful numerical methods often provide the only means to explore and analyse the PDEs. Various methods will be investigated with emphasis on the underlying ideas and principles of each method. This theoretical understanding will be underpinned by practical implementation of the numerical methods throughout the module. This approach will allow you to develop a well-grounded theoretical base as well as the necessary programming skills to implement solutions in real-life situations.
You will become conversant in the classification of PDEs as well as the stability and convergence of numerical schemes. Using this knowledge as a foundation, you will investigate and appraise state-of-the-art numerical methods. These may include but are not limited to
• Finite difference methods
• Finite element methods
• Finite volume methods
• Spectral methods
• Particle methods
How will I learn on this module?
You will learn the theory of ‘Numerical Solutions of Partial Differential Equations’ by attending regular lectures. You will become fluent in the various numerical techniques and programming skills through a series of homework (i.e. guided independent study) programming assignments that will count 50% towards the final mark. The other 50% comes from a final written, closed-book examination.
How will I be supported academically on this module?
You will be supported in the homework programming assignments, which will be assessed throughout the module and continuous formative feedback will be given. In addition to direct contact with the module team during scheduled lectures, you will be encouraged to develop your curiosity by making direct contact with the module team either via email or the open door policy operated throughout the programme. Supporting material will be placed on the e-learning portal of the university.
What will I be expected to read on this module?
All modules at Northumbria include a range of reading materials that students are expected to engage with. Online reading lists (provided after enrolment) give you access to your reading material for your modules. The Library works in partnership with your module tutors to ensure you have access to the material that you need.
What will I be expected to achieve?
Knowledge & Understanding:
1. You will be able to discern the appropriate numerical techniques for solving different types of partial differential equations.
2. You will be able to implement these techniques by creating and running computer codes and then critically appraise the numerical results.
Intellectual / Professional skills & abilities:
3. You will be able to develop algorithms through logical arguments, in order to solve various types of partial differential equations.
Personal Values Attributes (Global / Cultural awareness, Ethics, Curiosity) (PVA):
4. You will be able to work competently and independently against strict deadlines.
5. You will be able to communicate your solution methods and numerical results to both specialists and non-specialists.
How will I be assessed?
SUMMATIVE
1. Coursework (50%) – 1, 3, 5
(Assignment with set questions and problems – wordcount: max 1000 words + program code + graphs + plots + tables.)
2. Examination (50%) – 1, 2, 4, 5
(closed-book, written examination with set questions and problems)
Summative assessment is through the accumulated mark of all the coursework assignments (50%) as well as a formal examination at the end of the semester (50%).
FORMATIVE
You will be given formative feedback throughout by the tutor. Each homework assignment will be returned with written and oral feedback. Students will also receive personalised written exam feedback after the final examination.
Pre-requisite(s)
For MMath students:
KC5008 Ordinary and Partial Differential Equations
KC5000 Further Computational Mathematics
For MPHys students:
Co-requisite(s)
None
Module abstract
In ‘Numerical Solutions of Partial Differential Equations’ you will investigate various numerical techniques used to solve partial differential equations (PDEs). These powerful numerical methods often provide the only means to explore and analyse PDEs. The theoretical understanding and principles of each method will be underpinned by its practical implementation. This approach will allow you to develop a well-grounded theoretical base as well as the necessary programming skills to implement solutions in real-life situations.
You will be attending formal lectures and practical computer-based sessions during which you will become conversant with the theory and its aplications. Fluency in various numerical techniques and programming skills will follow from a series of homework programming assignments that will count 50% towards the final mark. The other 50% comes from a final written, closed-book examination. ‘Numerical Solutions of Partial Differential Equations’ is designed to provide students with a useful preparation for employment or further study in an applied mathematical or engineering environment.
Course info
UCAS Code F2W4
Credits 20
Level of Study Undergraduate
Mode of Study 4 years Full Time or 5 years with a placement (sandwich)/study abroad
Department Mathematics, Physics and Electrical Engineering
Location City Campus, Northumbria University
City Newcastle
Start September 2025
All information is accurate at the time of sharing.
Full time Courses are primarily delivered via on-campus face to face learning but could include elements of online learning. Most courses run as planned and as promoted on our website and via our marketing materials, but if there are any substantial changes (as determined by the Competition and Markets Authority) to a course or there is the potential that course may be withdrawn, we will notify all affected applicants as soon as possible with advice and guidance regarding their options. It is also important to be aware that optional modules listed on course pages may be subject to change depending on uptake numbers each year.
Contact time is subject to increase or decrease in line with possible restrictions imposed by the government or the University in the interest of maintaining the health and safety and wellbeing of students, staff, and visitors if this is deemed necessary in future.
Useful Links
Find out about our distinctive approach at
www.northumbria.ac.uk/exp
Admissions Terms and Conditions
northumbria.ac.uk/terms
Fees and Funding
northumbria.ac.uk/fees
Admissions Policy
northumbria.ac.uk/adpolicy
Admissions Complaints Policy
northumbria.ac.uk/complaints
