Numerical solution of partial differential equations

Overview

Partial differential equations describe some of the most important physical phenomena in nature and hence finding their solution is of enormous importance in real world applications. Depending on the type of equation, numerical methods of different flavours are most suitable. In this project, depending on the student’s background and interest, particular approaches including physics informed neural networks, spectral methods and particle-based methods may be employed.

Research engagement

Literature review, pen and paper mathematical derivations, computer coding, running numerical simulations

Research activities

The student will work with the supervisor to gain an understanding of the relevant equation and its importance in practical applications, and the most suitable numerical method for its solution. The student will develop computer code to implement a relevant numerical method for solving the equation and hence perform numerical simulations to verify its effectiveness and analyse the resulting solution.

Research skills

Familiarity with a relevant mathematical equation, numerical analysis, numerical simulation, computer coding

Outcomes

A working simulation computer code and analysis of its performance and/or analysis of aspects of the numerical solution

Skills and experience

The ideal candidate will have studied partial differential equations and be familiar with computer coding in a relevant language for numerical simulation

Start date

2 November, 2026

End date

19 February, 2027

Location

Gardens Point

Additional information

HPC resources are available

Contact

• Tim Moroney

3138 2262

t.moroney@qut.edu.au