Ruth Thomas

Senior Lecturer

Qualifications: BA, MA (Oxford), MSc, PhD (Manchester)

Room No. O16


Administrative Duties: Assistant Head of Department, Director of Undergraduate Studies, Undergraduate Tutor, Course Tutor for the Mathematics and Language Studies Degree Course.
Teaching: Currently, I am teaching the following lecture courses:

Approximation Theory and Numerical Integration (code: 322)

Numerical Solution of Ordinary Differential Equations (code: 362)

Advanced Ordinary Differential Equations (code: 463)

Research: My research interests are all in the area of numerical analysis. Currently, I am working on the following research projects:
  1. Numerical strategies for delay and Volterra differential algebraic equations. This is joint work with Professor Christopher Baker of the University of Manchester, and my research student, Carl Gibson.  This work has been supported by an EPSRC Research Grant.
  2. Numerical solution of periodic initial value problems with oscillatory solution. My research student, Muhammad Gul, is working with me on this project.  I am also working with Dr John Coleman of the University of Durham on deriving and developing collocation methods for problems of this type.
  3. Moving mesh methods for parabolic partial differential equations, in particular for problems arising when modelling the propagation of a narrow flame in a detonator delay element. Thebe Basebi, a research student, is working with me on this project.
  4. Numerical solution of Schrödinger's equation, in collaboration with Dr. Theodore Simos of the University of Thrace.
  5. Numerical solution of differential algebraic boundary value problems. This work has been supported by two EPSRC CASE studentships, in cooperation with ICI plc who had a particular interest in problems of this type arising in the modelling of detonation. 
Recent Publications
  • R M Thomas and M S H Khiyal.  Variable order, variable step methods for second order initial value problems.  Journal of Computational and Applied Mathematics, 79, 263-276 (1997).
  • R M Thomas and T E Simos.  A family of hybrid exponentially fitted predictor-corrector methods for the numerical integration of the radial Schrödinger equation.  Journal of Computational and Applied Mathematics, 87, 215-226 (1997).
  • C T H Baker, G A Bochorov, A Filiz, N J Ford, C A H Paul, F A Rihan, A Tang, R M Thomas, H Tian and D R Wille.  Numerical modelling by delay and Volterra functional differential equations.  In Topics in Computer Mathematics and its Applications (edited by E A Lipitakis), 113-137, LEA-Athens, Hellas (1999).
  • J A Sturgeon, R M Thomas and I Gladwell.  Solving a singular DAE model of unconfined detonation.  Computers and Chemistry  (To appear in 2000).


Dr R M Thomas
Mathematics Department, UMIST
P.O. Box 88
Manchester M60 1QD
UK
(0161) 200 3657 (use + 44 161 200 3657 from overseas)
Fax: (0161) 200 3669
Email: rmt@lanczos.ma.umist.ac.uk or Ruth.Thomas@umist.ac.uk