Quadratic RK shooting solution for a environmental parameter prediction boundary value problem
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 Boundary Value (BV) system. We study the numerical treatment of the resulting special quadratic form system using Shooting method. We compare the solutions of the problem when we employ a classical Singly Diagonally Implicit Runge Kutta (SDIRK) 4(3) pair of methods and a quadratic SDIRK 5(3) pair . Both pairs have the same computational costs whereas the second one attains higher order as it is specially constructed for quadratic problems.
 Publication:

International Conference of Computational Methods in Sciences and Engineering 2014 (ICCMSE 2014)
 Pub Date:
 October 2014
 DOI:
 10.1063/1.4897863
 Bibcode:
 2014AIPC.1618..839F