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

I. Famelis, G. Galanis and D. Triandafyllou

**Abstract**

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.

**Bibliography**

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[2]
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[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.