# Partial Differential Equations II - MAT00079M

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• Department: Mathematics
• Module co-ordinator: Dr. Henning Bostelmann
• Credit value: 10 credits
• Credit level: M
• Academic year of delivery: 2020-21

## Related modules

• None

### Prohibited combinations

Pre-requisite modules: students must have taken PDEs 1 - either MAT00040H or MAT00053M.

## Module will run

Occurrence Teaching cycle
A Spring Term 2020-21

## Module aims

• 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.).

## Module learning outcomes

• 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

## Module content

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 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.

## Assessment

Task Length % of module mark
Essay/coursework
Coursework
N/A 25
University - closed examination
Partial Differential Equations II
2 hours 75

None

### Reassessment

Task Length % of module mark
University - closed examination
Partial Differential Equations II
2 hours 100

## Module feedback

Current Department policy on feedback is available in the student handbook. Coursework and examinations will be marked and returned in accordance with this policy.