We are holding a two-day meeting to consider the influence that the work of John Crank has had on the numerical solution of time dependent PDEs, on the modelling of diffusive processes and on free boundary problems. The focus of the meeting will be on the state of the art of the subject and on future developments and applications, including industrial applications.
The programme (available here as a PDF or Word document - updated June 17, 2008), consists of invited talks and poster sessions and covers three themes:
Invited speakers include:
Although all the talks will be by invited speakers, we wish to encourage participants to present poster papers in poster sessions during the conference. Anyone wishing to submit a poster paper should follow the instructions below.
The Conference will be held on the Uxbridge campus of Brunel University. The fee for attendance will be £40.00 which will include morning coffee and afternoon tea on July 10th and 11th as well as all the materials for the Conference.
For those requiring it accommodation will be available in single study bedrooms with private en suite facilities in Lancaster/Gordon Halls of Residence on the Brunel University Uxbridge campus. This can be for any or all of the nights of July 9th, 10th and 11th. There will be a Conference Dinner in the Newton Room of the Hamilton Centre at Brunel University on the evening of July 10th. Conference participants will be able to purchase lunch on July 10th and 11th in the Hamilton Centre. Details of all costs are given in the fees section below.
Places at the Conference may be reserved by returning to us, preferably by fax to +44 1895 269732 a paper version of the registration document. This is available to download here either as a Word document or as a PDF file. Alternatively if you would like to be mailed a copy of the form please either write to us or send an email request to email@example.com. These forms should be returned as soon as possible and at the latest to reach BICOM by 13th June 2008. A detailed programme and abstracts of lectures/poster papers will be issued to those attending.
Research Students: The Conference has some limited funding to support research students studying at universities in the UK and the Republic of Ireland, who do not have other means of support (e.g. from their Doctoral Training Awards). Research students wishing to apply for support should submit a completed registration form as above, together with a letter of support from the supervisor.
Poster Papers: Participants wishing to present a poster paper should email a pdf file (maximum one A4 page) containing the title, authors name and affiliation, and the abstract of the poster to firstname.lastname@example.org as soon as possible, and in any case not later than 13th June 2008.
Bank Charges (if applicable) for non sterling cheques: £15
Cancellations received on or before 5th June will be refunded minus an administration charge of £25 per person. No fees can be refunded for cancellations received after 5th June 2008.
John Crank (1915 - 2006) specialised in the modelling and analysis of problems in diffusion. He originally worked in industry on the modelling and numerical solution of diffusion in polymers. In 1943 working together with Phyllis Nicolson on finite difference methods for the time dependent heat equation at the Courtaulds Research Laboratories, he discovered that suitably combining the finite difference replacements of the second-order space derivatives at two successive time steps yields a second-order implicit difference scheme which is stable for all values of the time and space step sizes. This work was published in 1947 and totally transformed worldwide the field of the numerical solution of time-dependent partial differential equations.
The Crank Nicolson method has since been incorporated universally and is now used routinely in contexts such as finite element methods in both the Continuous and Discontinuous Galerkin forms and in many fields additional to diffusion. In 1956 Crank published his monograph on The Mathematics of Diffusion, which has become a classic. In later years he moved into the field of free boundary problems, proposing in particular the famous oxygen diffusion and consumption moving boundary model problem, and in 1983 he published his last book, Free and Moving Boundary Value Problems.
John Crank was professor of Mathematics at Brunel University from 1964 until 1981. He died in October 2006, and we believe that it is now very timely to review his legacy and to consider the directions that the subject is taking and should take. We also believe that it is important that John Crank's style of interdisciplinary research into practical problems with industrial applications, employing clever ideas, should be emphasised and perpetuated. This is particularly true in research areas that have evolved rapidly over the last decade, such as numerical methods in finance and modelling in social science. An interdisciplinary meeting centred around the Crank legacy will provide a unique opportunity for mathematicians to influence research in these areas.