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, and will include an extended piece of coursework which will apply principles developed in the course to write a numerical solver for a partial differential equations problem. |
| 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
- Implementing numerical solvers for partial differential equations on a computer
|
Information for Visiting Students
| Pre-requisites | None |
| High Demand Course? |
Yes |
Course Delivery Information
|
| Academic year 2021/22, 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
80 %,
Coursework
20 %,
Practical Exam
0 %
|
| Additional Information (Assessment) |
Coursework 20% Exam 80% |
| Feedback |
Not entered |
| Exam Information |
| Exam Diet |
Paper Name |
Hours & Minutes |
|
| Main Exam Diet S2 (April/May) | MATH11207 Numerical Partial Differential Equations | 2:00 | |
Learning Outcomes
On completion of this course, the student will be able to:
- Study solutions to partial differential equations using numerical methods
- Discretise partial differential equations via the finite difference method
- Understand the principles of discretisation, consistency, stability, and accuracy
- Learn techniques for solving matrix systems resulting from the discretisation of differential equations
- Implement numerical solvers for partial differential equations in the Python programming language
|
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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