Differential equations with natural matrices coefficients

P Acosta-Humánez,J Ramírez-López

doi:10.1088/1742-6596/1514/1/012015

Abstract

In this paper we present the main results of the master thesis in applied mathematics of the second named author, which was supervised by the first named author. Such results, and for instance this paper, concerns to some differential and algebraic results involving natural matrices. The problem of solving differential equations is very ancient and is very important to get explicit solutions of differential equations to be applied in physics and other areas. In this paper, as well in the master thesis, we study the differential and algebraic structure of linear differential equations with natural matrix coefficients and generalizations. These results are original and important for researchers interested in differential algebra and applications of differential equations.

Highlights

In this paper is applied by the first time the concept of natural matrix with differential equations
As well in the master thesis, we study the differential and algebraic structure of linear differential equations with natural matrix coefficients and generalizations
This is a very important result in differential algebra because give us tools to solve more general differential equations arising in mathematical physics

Summary

Introduction

In this paper is applied by the first time the concept of natural matrix with differential equations. Combining some results of the both authors is presented this paper, the first paper in this line, with the aim of impacting the scientific community in differential algebra. The results of this research include that the differential Galois of linear differential systems with p-modified natural matrices, being p a polynomial, is isomorphic to the multiplicative group (C∗, ). This is a very important result in differential algebra because give us tools to solve more general differential equations arising in mathematical physics. Further developments concerning natural matrices correspond to [2,3,4,5], where the authors used Pasting and reversing in natural numbers [6,7] as well digital root [8]

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