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MA40171: Numerical solution of evolutionary equations

[Page last updated: 05 August 2021]

Academic Year: 2021/2
Owning Department/School: Department of Mathematical Sciences
Credits: 6 [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Masters UG & PG (FHEQ level 7)
Period:
Semester 1
Assessment Summary: CW 25%, EX 75%
Assessment Detail:
  • Coursework 1 (CW 13%)
  • Coursework 2 (CW 12%)
  • Examination (EX 75%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: Before taking this module you must take MA20222 AND take MA20223
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.

Programme availability:

MA40171 is Optional on the following programmes:

Department of Mathematical Sciences
  • RSMA-AFM16 : Integrated PhD Statistical Applied Mathematics
  • TSMA-AFM17 : MRes Statistical Applied Mathematics
  • TSMA-AFM16 : MSc Statistical Applied Mathematics
  • USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 3)
  • USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
  • USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
  • USMA-AFB13 : BSc(Hons) Mathematics (Year 3)
  • USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 4)
  • USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 4)
  • USMA-AFB05 : BSc(Hons) Statistics (Year 3)
  • USMA-AAB06 : BSc(Hons) Statistics with Study year abroad (Year 4)
  • USMA-AKB06 : BSc(Hons) Statistics with Year long work placement (Year 4)
  • USMA-AFM14 : MMath(Hons) Mathematics (Year 3)
  • USMA-AFM14 : MMath(Hons) Mathematics (Year 4)
  • USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 4)
  • USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)
  • USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 5)

Notes:

  • This unit catalogue is applicable for the 2021/22 academic year only. Students continuing their studies into 2022/23 and beyond should not assume that this unit will be available in future years in the format displayed here for 2021/22.
  • Programmes and units are subject to change 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.
  • Find out more about these and other important University terms and conditions here.