Meteorological data following two parameter Weibull distributions can be considered as statistical manifolds. The minimum distance between two elements of statistical manifold is defined by the corresponding geodesic, e.g., the minimum length curve that connects them. Such a curve satisfies a 2nd order quadratic Boundary Value (BV) system. In this work, we study the numerical solution of the resulting system using shooting method which uses Runge-Kutta integrators which are specially constructed for quadratic stiff ordinary differential equations. We employ a classical Singly Diagonally Implicit Runge-Kutta SDIRK 4(3) pair of methods and a quadratic SDIRK5(3) pair and compare their solutions. Both pairs have the same computational cost whereas the second one attains higher order as it is specially constructed for quadratic problems.

Boundary Value Problems (BVP), shooting method, quadratic Runge- Kutta, SDIRK, Information Geometry.