KC7017 - Numerical Solutions of Partial Differential Equations

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.

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.

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.

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.

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.

For MMath students:
KC5008 Ordinary and Partial Differential Equations
KC5000 Further Computational Mathematics
For MPHys students:

None

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.