Module Information
Module Identifier
MA34710
Module Title
Numerical Solution of Partial Differential Equations
Academic Year
2019/2020
Co-ordinator
Semester
Semester 2
Pre-Requisite
Other Staff
Course Delivery
| Delivery Type | Delivery length / details |
|---|---|
| Lecture | 12 x 1 Hour Lectures |
| Practical | 5 x 2 Hour Practicals |
Assessment
| Assessment Type | Assessment length / details | Proportion |
|---|---|---|
| Semester Exam | 2 Hours | 50% |
| Semester Assessment | Report 1 on numerical implementation of the finite difference method (2000 words). | 25% |
| Semester Assessment | Report 2 on numerical implementation of the finite difference method (2000 words). | 25% |
| Supplementary Exam | 2 Hours | 100% |
Learning Outcomes
On successful completion of this module students should be able to:
1. Discretise elliptic, hyperbolic and parabolic partial differential equations using finite difference methods.
2. Use the variational formulation to derive a finite element discretisation of a PDE.
3. Perform an error and convergence analysis for these discrete approximations to PDEs.
4. Solve an elliptic or parabolic PDE numerically using different computational methods.
Brief description
This module provides an introduction to numerical methods for solving partial differential equations of elliptic and parabolic type. Concepts such as consistency, convergence and stability of numerical methods will be discussed.
Content
Finite difference approximations to elliptic, hyperbolic and one-dimensional parabolic partial differential equations. Local truncation error and error analysis.
Variational formulation and the finite element method. Convergence and stability.
Numerical implementation of these methods.
Variational formulation and the finite element method. Convergence and stability.
Numerical implementation of these methods.
Module Skills
| Skills Type | Skills details |
|---|---|
| Application of Number | Inherent in module. |
| Communication | The written reports will require students to clearly explain their findings. |
| Improving own Learning and Performance | Problem sheets will allow students to assess their progress. |
| Personal Development and Career planning | Familiarity with numerical methods for solving differential equations is a valuable career skill, particularly for those going on to work in finance and in industry. |
| Problem solving | Inherent in module. |
| Subject Specific Skills | Inherent in module. |
| Team work | Students will be encouraged to work in groups for the practical sessions. |
Notes
This module is at CQFW Level 6