Computational Modelling and Programming module (MA51004)

Mathematical models in most areas of science and engineering generate ordinary, stochastic, and partial differential equations (ODEs, SDEs, and PDEs) that often have to be solved numerically. Some typical examples include systems of particles such as stars, cells, and atoms, population dynamics, cooling systems in power stations, chemical reactions, and stock option pricing. Computational modelling and programming provide approximation methods for numerical solutions to mathematical models.  

In this module, you will learn to apply built-in “black box” solvers in MATLAB and COMSOL to some of the above mathematical models. To better understand the inner workings of these tools, you will be given a brief introduction to stiff ODEs, stochastic processes and stochastic ODEs through examples and finite element methods (FEMs). You will also learn to “hand code” basic ODE, SDE and PDE solution methods. This module will develop your numerical analysis and scientific computing skills for simulations of scientific and engineering problems and prepare you to explore core areas of applied and computational mathematics.  

Topics include:  

• MATLAB ODE solvers for initial value problems  
• MATLAB for random variables, stochastic processes and SDEs  
• MATLAB for ODE boundary value problems  
• MATLAB for PDEs  
• Weak formulations for PDEs  
• FEMs and COMSOL fundamentals.