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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Numerical Ordinary Differential Equations and Applications (MATH10060)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 10 (Year 3 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryMost 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.
Course description 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.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: ( Honours Differential Equations (MATH10066) OR Dynamics and Vector Calculus (PHYS08043)) AND ( Computing and Numerics (MATH08065) OR Computer Simulation (PHYS08026) OR Programming and Data Analysis (PHYS08049))
Prohibited Combinations Other requirements None
Information for Visiting Students
Pre-requisitesVisiting students are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling.
High Demand Course? Yes
Course Delivery Information
Academic year 2020/21, Available to all students (SV1) Quota:  None
Course Start Semester 2
Timetable Timetable
Learning and Teaching activities (Further Info) Total Hours: 100 ( Lecture Hours 22, Seminar/Tutorial Hours 10, Summative Assessment Hours 2, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 64 )
Assessment (Further Info) Written Exam 50 %, Coursework 50 %, Practical Exam 0 %
Additional Information (Assessment) Coursework 50%, Examination 50%
Feedback Not entered
Exam Information
Exam Diet Paper Name Hours & Minutes
Main Exam Diet S2 (April/May)Numerical Ordinary Differential Equations and Applications (MATH10060) 1:30
Learning Outcomes
On completion of this course, the student will be able to:
  1. determine appropriate numerical methods to solve a range of ODEs.
  2. implement such numerical methods in a suitable programming language.
  3. derive and analyse such methods and their errors.
  4. understand the principles of consistency, stability and convergence.
  5. apply the above to examples from modern applied mathematics.
Reading List
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,
Springer 2010

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
Additional Information
Graduate Attributes and Skills Not entered
Course organiserProf Desmond Higham
Tel: (0131 6)50 6018
Course secretaryMr Christopher Palmer
Tel: (0131 6)50 5060
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