MA40171: Numerical solution of evolutionary equations
[Page last updated: 23 October 2023]
Academic Year:  2023/24 
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:  CWRI 25%, EXCB 75% 
Assessment Detail: 
 Coursework (CWRI 25%)
 Examination (EXCB 75%)

Supplementary Assessment: 
 Likeforlike reassessment (where allowed by programme regulations)

Requisites: 
Before taking this module you must take MA20222 AND take MA20223

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.

Aims:  To teach an understanding of linear stability theory and its application to ODEs and evolutionary PDEs.

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 onestep method; stability and convergence. Introduction to physically relevant PDEs. Wellposed 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.

Course availability: 
MA40171 is Optional on the following courses:
Department of Mathematical Sciences
 RSMAAFM16 : Integrated PhD Statistical Applied Mathematics
 TSMAAFM17 : MRes Statistical Applied Mathematics
 TSMAAFM16 : MSc Statistical Applied Mathematics
 USMAAFB15 : BSc(Hons) Mathematical Sciences (Year 3)
 USMAAAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
 USMAAKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
 USMAAFB13 : BSc(Hons) Mathematics (Year 3)
 USMAAAB14 : BSc(Hons) Mathematics with Study year abroad (Year 4)
 USMAAKB14 : BSc(Hons) Mathematics with Year long work placement (Year 4)
 USMAAAB06 : BSc(Hons) Statistics with Study year abroad (Year 4)
 USMAAKB06 : BSc(Hons) Statistics with Year long work placement (Year 4)
 USMAAFM14 : MMath(Hons) Mathematics (Year 3)
 USMAAFM14 : MMath(Hons) Mathematics (Year 4)
 USMAAAM15 : MMath(Hons) Mathematics with Study year abroad (Year 4)
 USMAAKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)
 USMAAKM15 : MMath(Hons) Mathematics with Year long work placement (Year 5)

Notes:  This unit catalogue is applicable for the 2023/24 academic year only. Students continuing their studies into 2024/25 and beyond should not assume that this unit will be available in future years in the format displayed here for 2023/24.
 Courses 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 prerequisite rules.
 Find out more about these and other important University terms and conditions here.
