MA40171: Numerical solution of evolutionary equations
[Page last updated: 09 August 2024]
| Academic Year: | 2024/25 |
| 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
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| Assessment Summary: | CWRI 25%, EXCB 75% |
| Assessment Detail: |
- Coursework (CWRI 25%)
- Examination (EXCB 75%)
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| Supplementary Assessment: |
- Like-for-like reassessment (where allowed by programme regulations)
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| Requisites: |
Before taking this module you must take MA20222 AND take MA20223
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| 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.
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| Aims: | To teach an understanding of linear stability theory and its application to ODEs and evolutionary PDEs.
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| Skills: | Understanding of the finite element method (T, A), Computer programming with the finite element method (T, A).
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| 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.
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| Course availability: |
MA40171 is Optional on the following courses:
Department of Mathematical Sciences
- RSMA-AFM18 : Integrated PhD 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-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)
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Notes: - This unit catalogue is applicable for the 2024/25 academic year only. Students continuing their studies into 2025/26 and beyond should not assume that this unit will be available in future years in the format displayed here for 2024/25.
- 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 pre-requisite rules.
- Find out more about these and other important University terms and conditions here.
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