SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Contributed Talk

Show full list of Contributed Talks Show talk context (CS14)

The numerical solution of a BVP which rises in the prediction of meteorological parameters.

I. Famelis, G. Galanis and D. Triandafyllou

Using tools of Information Geometry, the minimum distance between two elements of a statistical manifold is defined by the corresponding geodesic, e.g. the minimum length curve that connects them. Such a curve, where the probability distribution functions in the case of our meteorological data are two-parameter Weibull distributions, satisfies a 2${}^{nd}$ order quadratic BVP system. This system can be solved by finite differences employing Newton's method or quasi-Newton methods for the resulting nonlinear system and taking into consideration the special form of the Jacobian matrix. Another approach is to use MIRK formulas to get a solution of the problem. As the problem is quadratic MIRK schemes constructed for such problems can be considered. This research has been co-funded by the European Union and Greek nat. resources under the framework of the "Archimedes III: Funding of Research Groups in TEI of Athens" project of the "Education and Lifelong Learning" Op. Progr.

[1] S-I. Amari and H. Nagaoka. Methods of Information Geometry, American Mathematical Society, Oxford University Press, Oxford 2000.
[2] C. Brezinski, A classification of quasi-Newton methods, Numer Algor (1997), 33, pp. 123-135.
[3] W. H. Enright and P. H. Muir, Runge-Kutta Software With Defect Control For Boundary Value ODES, SIAM J. Sci. Comput. (1996), 17, 2, pp. 479-497.
[4] L.F. Shampine et. al. , A User-Friendly Fortran BVP Solver, JNAIAM (2006), 1, 2, pp. 201-217.
[5] A. Iserles et. al. Runge Kutta methods for quadratic ODEs, BIT (1998), 38, 2, pp. 315-346.

Organized by         Universidad de Valladolid     IMUVA