KC7017 - Numerical Solutions of Partial Differential Equations

APPLY NOW BOOK AN OPEN DAY Add to My Courses Register your interest / Course PDF

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 the following numerical methods:

• Finite difference methods
• Finite element methods
• Finite volume methods
• Spectral methods
• Particle methods
• Numerical methods for solving nonlinear PDEs
• Numerical methods for solving PDEs in conservative form

Evaluating each numerical method in depth, you will be able to make informed choices when selecting the optimal solution method for different types of PDEs. Also, you will become proficient in writing and implementing computer codes (e.g. using MATLAB) by solving the various types of PDEs.

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. The reading list for this module can be found at: http://readinglists.northumbria.ac.uk
(Reading List service online guide for academic staff this containing contact details for the Reading List team – http://library.northumbria.ac.uk/readinglists)

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 in both written and oral form to both specialists and non-specialists.

How will I be assessed?

SUMMATIVE
1. Assignment (50%) – 1, 2, 3, 4, 5
2. Examination (50%) – 1, 2, 3, 4, 5

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%).

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)

KC5008 Ordinary and Partial Differential Equations
KC5000 Further Computational Mathematics

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 during which you will become conversant with the theory. 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 G101

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 2020

Fee Information

Module Information

Current, Relevant and Inspiring

We continuously review and improve course content in consultation with our students and employers. To make sure we can inform you of any changes to your course register for updates on the course page.

Your Learning Experience 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