Postgraduate Course: Numerical Partial Differential Equations with Applications (MATH11191)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 11 (Postgraduate) |
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 |
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.
- Finite difference discretisation
- The method of lines
- Consistency, stability, and convergence
- Methods for proving numerical stability
- Galerkin finite element discretisation
- Boundary conditions
- Discretisation matrices
- Writing numerical solvers for partial differential equations using Matlab
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Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
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Co-requisites | |
| Prohibited Combinations | |
Other requirements | Students NOT on the MSc in Computational Applied Mathematics programme MUST have passed Honours Differential Equations (MATH10066) AND Computing and Numerics (MATH08065) |
Information for Visiting Students
| Pre-requisites | None |
| High Demand Course? |
Yes |
Course Delivery Information
| Not being delivered |
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
- Discretise weak form partial differential equations via the finite element method
- Understand the principles of discretisation consistency, stability, and accuracy
- Develop numerical solvers for partial differential equations
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Reading List
| "Finite Difference Methods for Ordinary and Partial Differential Equations" by Randall J LeVeque. |
Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | NPDEA |
Contacts
| Course organiser | Dr James Maddison
Tel: (0131 6)50 5036
Email: j.r.maddison@ed.ac.uk |
Course secretary | Miss Sarah McDonald
Tel: (0131 6)50 5043
Email: sarah.a.mcdonald@ed.ac.uk |
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