Module Identifier MA34710
Module Title NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS
Co-ordinator Professor Russell Davies
Semester Intended for use in future years
Next year offered N/A
Next semester offered N/A
Other staff Professor Russell Davies
Pre-Requisite MA25110
Co-Requisite MA30210
Course delivery Lecture   19 x 1 hour lectures
Seminars / Tutorials   3 x 1 hour example classes
Assessment
Assessment TypeAssessment Length/DetailsProportion
Semester Exam2 Hours (written examination)  100%
Supplementary Assessment2 Hours (written examination)  100%

#### Learning outcomes

On completion of this module, a student should be able to:
1. discretise an elliptic partial differential equation using and finite element methods;
2. perform an error analysis for the discrete approximation to elliptic equations;
3. discretise hyperbolic and parabolic partial differential equations in one space variable;
• perform an error analysis for the discrete approximation to hyperbolic and parabolic equations.

#### Brief description

Partial differential equations are the main means of providing mathematical models in science, engineering and other fields. Generally these models must be solved numerically. This course provides an introduction to numerical techniques for eliiptical and parabolic equations.

#### Aims

The aim of this course is to provide an introduction to numerical methods for solving partial differential equations of elliptic, hyperbolic and parabolic type. Concepts such as consistency, convergence and stability of numerical methods will be discussed. Fourier methods will be used to analyse stability and convergence of finite difference methods, while finite element methods will be analysed in terms of interpolation error estimates.

#### Content

1. Variational formulation and the finite element method. Finite element spaces and interpolation.
2. Finite difference approximations to hyperbolic and parabolic partial differential equations in one space variable. Local truncation error and error analysis. Explicit and implicit methods. Convergence and stability. The Thomas algorithm.