Pre-requisite modules
Co-requisite modules
- None
Prohibited combinations
Pre-requisite modules: students must have taken PDEs 1 - either MAT00040H or MAT00053M.
Occurrence | Teaching cycle |
---|---|
A | Spring Term 2022-23 |
To give an introduction to numerical methods for solving partial differential equations (PDEs) and to show how numerical algorithms can be implemented in practice.
To analyse the error of various numerical algorithms for solving PDEs and discuss practical problems that arise when we apply these algorithms.
To illustrate numerical methods by solving real problems from various areas of natural sciences such as physics, biology, fluid mechanics, etc.).
know basic finite-difference methods for solving partial differential equations
be able to analyse the error for a particular numerical method and appreciate the efficiency in implementation of numerical algorithms
be able to obtain numerical solutions of simple PDEs with the help of MATLAB
Syllabus
Finite-differences, truncation error, convergence and stability.
Explicit and implicit finite-difference schemes for parabolic PDEs. The alternating-direction method.
Finite-difference schemes for elliptic PDEs. Relaxation methods.
Finite-difference methods for hyperbolic PDEs: explicit and implicit schemes for wave equation; Lax-Wendroff scheme for hyperbolic systems.
Spectral methods: polynomial interpolation on Chebyshev points; Chebyshev differentiation matrices; boundary value problems. (These more advanced topics are not taught in the H-level variant of this module.)
Academic and graduate skills
Academic skills: the numerical techniques taught are used in many areas of applied mathematics.
Graduate skills: through lectures, examples, computer classes, students will develop their ability to assimilate, process and engage with new material quickly and efficiently. They develop problem solving-skills and learn how to apply techniques to unseen problems. Students on this module will learn to work more independently and assimilate advanced material at a greater rate than those on the H-level variant.
Task | Length | % of module mark |
---|---|---|
Closed/in-person Exam (Centrally scheduled) Partial Differential Equations II |
2 hours | 75 |
Essay/coursework Project 1 |
N/A | 10 |
Essay/coursework Project 2 |
N/A | 15 |
None
Task | Length | % of module mark |
---|---|---|
Closed/in-person Exam (Centrally scheduled) Partial Differential Equations II |
2 hours | 100 |
Current Department policy on feedback is available in the student handbook. Coursework and examinations will be marked and returned in accordance with this policy.
W F Ames, Numerical Methods for Partial Differential Equations, Academic Press, 1977 (S 7.383 AME).
L N Trefethen, Spectral methods in MATLAB, SIAM, 2000 (S 7.83 TRE).