Undergraduate Course: Numerical Ordinary Differential Equations and Applications (MATH10060)
|School||School of Mathematics
||College||College of Science and Engineering
|Credit level (Normal year taken)||SCQF Level 10 (Year 3 Undergraduate)
||Availability||Available to all students
|Summary||Most ordinary differential equations (ODEs) lack solutions that can be given in explicit analytical formulas. Numerical methods for ODEs allow for the computation of approximate solutions and are essential for their quantitative study. In some cases, a numerical method can facilitate qualitative analysis as well, such as probing the long term solution behaviour. As well as studying the theory, the course has a strong emphasis on implementation of these methods (in Python) to tackle modern applications of ODEs.
This course begins by introducing basic numerical schemes, such as Euler's method, including a study of their derivation and convergence properties. It then discusses more accurate approaches such as Taylor series methods, numerical quadrature, and Runge-Kutta schemes, in terms of both their theoretical properties and practical implementation. The related ideas of consistency, stability and convergence of numerical methods will then be studied, as well as the corresponding order conditions for Runge-Kutta schemes.
Motivated by a range of applications, more advanced techniques such as variable step size methods and linear multi-step approaches will be developed, again studying both theoretical and practical aspects.
Finally, more specialised schemes will be presented. These are strongly application-dependent and could include geometric integration, symplectic methods, splitting schemes, shooting methods, or techniques for tackling differential-algebraic equations.
There is a strong focus on modern applications and numerical implementation throughout the course, which will serve to enhance existing programming skills and broaden knowledge of modern areas of applied mathematics.
Information for Visiting Students
|Pre-requisites||Visiting students are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling.
|High Demand Course?
Course Delivery Information
|Academic year 2020/21, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
Lecture Hours 22,
Seminar/Tutorial Hours 10,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
|Assessment (Further Info)
|Additional Information (Assessment)
||Coursework 50%, Examination 50%
||Hours & Minutes
|Main Exam Diet S2 (April/May)||Numerical Ordinary Differential Equations and Applications (MATH10060) ||2:00|
On completion of this course, the student will be able to:
- determine appropriate numerical methods to solve a range of ODEs.
- implement such numerical methods in a suitable programming language.
- derive and analyse such methods and their errors.
- understand the principles of consistency, stability and convergence.
- apply the above to examples from modern applied mathematics.
|An electronic set of lecture notes will be provided. Students may find the following useful:|
D. Griffiths and D. Higham, Numerical Methods for Ordinary Differential Equations,
A. Iserlies, A First Course in the Numerical Analysis of Differential Equations, Cambridge University Press, 2008
L. N. Trefethen, Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations
|Graduate Attributes and Skills
|Course organiser||Prof Desmond Higham
Tel: (0131 6)50 6018
|Course secretary||Mr Christopher Palmer
Tel: (0131 6)50 5060