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Analysis of singularities and of integrability of ODE's by algorithms of Power Geometry

Alexander D. Bruno (2011)

Banach Center Publications

Here we present basic ideas and algorithms of Power Geometry and give a survey of some of its applications. In Section 2, we consider one generic ordinary differential equation and demonstrate how to find asymptotic forms and asymptotic expansions of its solutions. In Section 3, we demonstrate how to find expansions of solutions to Painlevé equations by this method, and we analyze singularities of plane oscillations of a satellite on an elliptic orbit. In Section 4, we consider the problem of local...

Analysis of The Impact of Diabetes on The Dynamical Transmission of Tuberculosis

D.P. Moualeu, S. Bowong, J.J. Tewa, Y. Emvudu (2012)

Mathematical Modelling of Natural Phenomena

Tuberculosis (TB) remains a major global health problem. A possible risk factor for TB is diabetes (DM), which is predicted to increase dramatically over the next two decades, particularly in low and middle income countries, where TB is widespread. This study aimed to assess the strength of the association between TB and DM. We present a deterministic model for TB in a community in order to determine the impact of DM in the spread of the disease....

Analytic enclosure of the fundamental matrix solution

Roberto Castelli, Jean-Philippe Lessard, Jason D. Mireles James (2015)

Applications of Mathematics

This work describes a method to rigorously compute the real Floquet normal form decomposition of the fundamental matrix solution of a system of linear ODEs having periodic coefficients. The Floquet normal form is validated in the space of analytic functions. The technique combines analytical estimates and rigorous numerical computations and no rigorous integration is needed. An application to the theory of dynamical system is presented, together with a comparison with the results obtained by computing...

Analytic solution of transcendental equations

Henryk Górecki (2010)

International Journal of Applied Mathematics and Computer Science

A decomposition technique of the solution of an n-th order linear differential equation into a set of solutions of 2-nd order linear differential equations is presented.

Aperiodicity of the Hamiltonian flow in the Thomas-Fermi potential.

Charles L. Fefferman, Luis A. Seco (1993)

Revista Matemática Iberoamericana

In [FS1] we announced a precise asymptotic formula for the ground-state energy of a non-relativistic atom. The purpose of this paper is to establish an elementary inequality that plays a crucial role in our proof of that formula. The inequality concerns the Thomas-Fermi potentialVTF = -y(ar) / r, a > 0, where y(r) is defined as the solution of⎧   y''(x) = x-1/2y3/2(x),⎨   y(0) = 1,⎩   y(∞) = 0.

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