Numerical methods for differential equations

Prerequisite:

Numerical Analysis (X01NUM)
Computer Algebra Systems (X01PAS)

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

The course covers basic methods related to numerical solution of differential equations:

Numerical solution of linear systems, interpolation, numerical differentiation

and numerical integration. Numerical solution of initial and boundary value problems

for ordinary differential equations. Short introduction to the theory of partial

differential equations. Numerical solution of elliptic, parabolic and hyperbolic problems. Some exercises make use of MATLAB numerical computing environment.

Requirements:

Syllabus of lectures:

1. Numerical solution of linear systems - direct and iterative methods.

2. Gradient methods. Matrix inversion.

3. Interpolation. Numerical differentiation.

4. Numerical integration.

5. Numerical solution of initial value problems for ordinary differential equations - one-step methods.

6. Multi-step methods.

7. Numerical solution of boundary value problems for ordinary differential equations - reduction to initial value problems.

8. Finite difference method.

9. Introduction to the theory of partial differential equations.

10. Numerical solution of elliptic problems - finite difference method.

11. Variational methods, finite element method.

12. Numerical solution of parabolic problems.

13. Numerical solution of hyperbolic problems.

14. Back-up class.

Syllabus of tutorials:

1. Introduction to MATLAB.

2. Numerical solution of linear systems.

3. Numerical solution of linear systems - MATLAB.

4. Interpolation, numerical differentiation and integration.

5. Interpolation, numerical differentiation and integration - MATLAB.

6. Numerical solution of initial value problems for ordinary differential equations.

7. Numerical solution of initial value problems for ordinary differential equations - MATLAB.

8. Numerical solution of boundary value problems for ordinary differential equations.

9. Numerical solution of boundary value problems for ordinary differential equations - MATLAB.

10. Numerical solution of elliptic problems.

11. Numerical solution of elliptic problems - MATLAB.

12. Numerical solution of parabolic and hyperbolic problems.

13. Numerical solution of parabolic and hyperbolic problems - MATLAB.

14. Back-up class.

Study Objective:

The aim of the course is to introduce students into basic numerical methods related to solution of ordinary and partial differential equations.

Study materials:

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: