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MA40171: Numerical solution of evolutionary equations

Follow this link for further information on academic years Academic Year: 2015/6
Further information on owning departmentsOwning Department/School: Department of Mathematical Sciences
Further information on credits Credits: 6
Further information on unit levels Level: Masters UG & PG (FHEQ level 7)
Further information on teaching periods Period: Semester 1
Further information on unit assessment Assessment Summary: CW 25%, EX 75%
Further information on unit assessment Assessment Detail:
  • Coursework 1 (CW 13%)
  • Coursework 2 (CW 12%)
  • Examination (EX 75%)
Further information on supplementary assessment Supplementary Assessment: MA40171 Mandatory extra work (where allowed by programme regulations)
Further information on requisites Requisites: Before taking this module you must take MA20222 AND ( take MA30044 OR take MA30063 OR take MA30170 )
Further information on descriptions Description: Aims:
To teach an understanding of linear stability theory and its application to ODEs and evolutionary PDEs.

Learning Outcomes:
The students should be able to analyse the stability and convergence of a range of numerical methods and assess the practical performance of these methods through computer experiments.

Skills:
Understanding of the finite element method (T, A), Computer programming with the finite element method (T, A).

Content:
Solution of initial value problems for ODEs by Linear Multistep methods: local accuracy, order conditions; formulation as a one-step method; stability and convergence. Introduction to physically relevant PDEs. Well-posed problems. Truncation error; consistency, stability, convergence and the Lax Equivalence Theorem; techniques for finding the stability properties of particular numerical methods. Numerical methods for parabolic and hyperbolic PDEs.
Further information on programme availabilityProgramme availability:

MA40171 is Optional on the following programmes:

Department of Mathematical Sciences
Notes:
* This unit catalogue is applicable for the 2015/16 academic year only. Students continuing their studies into 2016/17 and beyond should not assume that this unit will be available in future years in the format displayed here for 2015/16.
* Programmes and units are subject to change at any time, in accordance with normal University procedures.
* Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.