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Semester 2

Numerical Ordinary Differential Equations and Applications (MATH10060)

Subject

Mathematics

College

SCE

Credits

10

Normal Year Taken

3

Delivery Session Year

2023/2024

Pre-requisites

Visiting students are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling.

Course 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.

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. Similarly, the class of linear multi-step methods will be introduced, and their properties studiedThere 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.

Assessment Information

Written Exam 80%, Coursework 20%, Practical Exam 0%

Additional Assessment Information

Coursework 20%, Examination 80%

view the timetable and further details for this course