Undergraduate Course: Numerical Partial Differential Equations (MATH11207)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 11 (Year 5 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 10 |
ECTS Credits | 5 |
| Summary | This course introduces the numerical discretisation of partial differential equations. A number of different partial differential equations will be considered, and methods for yielding approximate numerical solutions will be studied. The course makes significant use of tools from linear algebra. |
| Course description |
Syllabus:
- Finite difference discretisation
- The method of lines
- Consistency, stability, and convergence
- Methods for proving numerical stability
- Boundary conditions
- Discretisation matrices
- Linear algebra solvers for matrix systems arising from discretisations
|
Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
Students MUST have passed:
Honours Differential Equations (MATH10066)
|
Co-requisites | |
| Prohibited Combinations | |
Other requirements | Note that PGT students on School of Mathematics MSc programmes are not required to have taken pre-requisite courses, but they are advised to check that they have studied the material covered in the syllabus of each pre-requisite course before enrolling. |
Information for Visiting Students
| Pre-requisites | This is a Year 4/5 advanced, Honours level course. Visiting students are expected to have an academic profile equivalent to at least the first three years of the BSc (Hons) Mathematics programme (UTMATHB), and should be confident that their background has equipped them to undertake a course at this level. Students should have passed courses equivalent to Honours Differential Equations (MATH10066). |
| High Demand Course? |
Yes |
Course Delivery Information
|
| Academic year 2026/27, Available to all students (SV1)
|
Quota: None |
| Course Start |
Semester 2 |
Timetable |
Timetable |
| Learning and Teaching activities (Further Info) |
Total Hours:
100
(
Lecture Hours 22,
Seminar/Tutorial Hours 6,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
68 )
|
| Assessment (Further Info) |
Written Exam
100 %,
Coursework
0 %,
Practical Exam
0 %
|
| Additional Information (Assessment) |
Effective from 2026/27: Coursework 0% Exam 100% |
| Feedback |
Not entered |
| Exam Information |
| Exam Diet |
Paper Name |
Minutes |
|
| Main Exam Diet S2 (April/May) | MATH11207 Numerical Partial Differential Equations | 120 | |
Learning Outcomes
On completion of this course, the student will be able to:
- Construct discretisations for time-dependent partial differential equations using the finite difference method.
- Construct discretisations for time-dependent partial differential equations using the method of lines.
- Apply the principles of consistency, stability, and convergence to assess the performance of discretisations of partial differential equations.
- Apply appropriate techniques to solve linear systems resulting from the discretisation of partial differential equations.
|
Reading List
| Randall J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems, SIAM. |
Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | NPDE,Partial Differential Equations |
Contacts
| Course organiser | Dr John Pearson
Tel: (0131 6)50 5049
Email: J.Pearson@ed.ac.uk |
Course secretary | Mr Martin Delaney
Tel: (0131 6)50 6427
Email: Martin.Delaney@ed.ac.uk |
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