Ordinary Differential Equations and the Approximation module (MA41003)

About the module

Ordinary Differential Equations (ODEs) are an important modelling tool in Science and Engineering. These can rarely be solved exactly and so techniques have been developed to derive approximate solutions that may, in principle, be made as accurate as desired. This module, aimed at Level 4 students, will investigate these techniques. This module is mandatory for Level 4 students taking a BSc or MSci in Mathematical Biology, or an MSci in Mathematics and Physics. This module may be taken in combination with other Level 3 or 4 modules by other Level 4 students. If you have questions about this module or the possible combinations, please contact your Advisor of Studies.

Prerequisites

Students taking this module must have achieved a pass mark in each of the modules MA31002 and either MA31007 or MA32002, or equivalents.

Indicative Content

• Numerical methods for initial value problems for ODEs

  Taylor Series Methods; Linear multi-step methods: one-step methods (Euler, Trapezoidal and Backward Euler methods) and two-step methods; Consistency, zero-stability, weak stability theory and A-stability; Provision of the extra starting values and the potential for instability; Runge-Kutta methods: construction and weak stability theory; Application to systems.

• Boundary value problems for ODEs

  BVPs for second order ODEs; eigenvalues and eigenfunctions; orthogonality; Green′s functions and maximum principles; Finite difference methods: 2nd order methods; Treatment of boundary conditions; Discrete maximum principles; Convergence.

Delivery and Assessment

The module is delivered in the form of lectures and workshops/tutorials and assessed via an exam (80%) and coursework (20%).

Credit Rating

This module is a Scottish Higher Education Level 4 or SCQF level 10 module and is rated as 15 SCOTCAT credits or 7.5 ECTS credits.