||To introduce students to some current research problems
of importance in
the solution of differential equations.
||On successful completion of this module, students will
be able to:
- Develop numerical methods for solving
differential-algebraic equations, delay differential equations,
Hamiltonian problems and high order differential equations.
- Identify numerical methods that preserve
the qualitative behaviour of the solution of the problem.
- Recognise some of the numerical
difficulties that can occur when solving problems arising in
scientific and industrial applications.
||157, 211, 362 (ex-UMIST)
||This module introduces some topics from the field of ordinary
differential equations, in which there has been much research activity recently. The
module begins by discussing the numerical solution of differential-algebraic equations
(DAEs), consisting of coupled systems of ordinary differential equations (ODEs) and
algebraic equations. Next, differential equations with delay terms are introduced.
Features such as the propagation of discontinuities are discussed and numerical methods
for solving such problems are described. Then, the numerical solution of Hamiltonian
problems is discussed. The property of symplecticness characterises Hamiltonian problems
and we investigate numerical methods that preserve this property. Finally, for MMath
students only, we consider the numerical solution of higher order differential equations.
||E Hairer, S P Norsett and G Wanner, Ordinary Differential
Equations I: Nonstiff Problems, (2nd edition), 1993, Springer-Verlag.
||E Hairer and G Wanner, Solving Ordinary Differential
Equations II: Stiff and Differential Algebraic Problems, (2nd edition), 1996,
(for MMath); 25% (for MSc)
||Coursework Mode: Project, set in Week 2, deadline in Week 9.
(for MMath); 75% (for MSc)
||For MMath students, the examination is of 2 hours duration at
the end of the Second Semester.
||For MSc students, the examination is of one and a half hours
duration in April.