MTH3340 - Numerical methods for partial differential equations

Overview

Partial differential equations are ubiquitous in many domains of sciences and industry, as they model phenomena with spatial and temporal variations. Most of these models are too complex to be exactly solved, and numerical methods are the only way to gather quantitative behaviour on the solutions. This unit covers the design, analysis and implementation of numerical methods for partial differential equations. Topics covered can include finite difference methods, finite element methods, finite volume methods, error analysis, elliptic equations, parabolic equations, implementation in dynamic languages (such as Python or Julia). The focus will be on the design of the methods, their mathematical analysis, and their implementation and numerical testing.

Offerings

S2-01-CLAYTON-ON-CAMPUS

Rules

Enrolment Rule

Contacts

Chief Examiner(s)

Professor Santiago Badia

Unit Coordinator(s)

Professor Santiago Badia

Learning outcomes

On successful completion of this unit, you should be able to:

Demonstrate understanding of the need for numerical methods to gather quantitative information on the solutions to partial differential equations.

Design and analyse the convergence and stability of numerical methods for a range of partial differential equations.

Select appropriate discretisation techniques based on their particular features, and the features of the considered model.

Implement specific numerical methods in a high-level language (such as Python or Julia), and interpret numerical outputs.

Demonstrate advanced skills in the written and oral presentation of theoretical and practical numerical problems involving partial differential equations.

Teaching approach

Active learning

We will use a blend of lectures, applied classes and labs. Lectures will enable us, as usual in mathematics, to deliver the main content of the unit – albeit in an interactive way, questioning student’s understanding and welcoming questions from students. Applied classes revolve around students actively solving exercises, putting in practice the content covered in the lectures; this is an essential way of assimilating that content. Labs will be focused around practical implementation of the methods, the issues around those and the interpretation of the numerical outputs.

Assessment

1 - Continuous assessment

2 - Final assessment - Exam (3 hours and 10 minutes)

Scheduled and non-scheduled teaching activities

Applied sessions

Seminars

Workload requirements

Workload

Availability in areas of study

Applied mathematics
Pure mathematics
Mathematics
Mathematical statistics