arXiv subjects

John Michael Nahay

Publications and source records attributed to John Michael Nahay.

2 recordsLinked to original sources

arXiv2008

Solving polynomial differential equations by transforming them to linear functional-differential equations

We present a new approach to solving polynomial ordinary differential equations by transforming them to linear functional equations and then solving the linear functional equations. We will focus most of our attention upon the first-order Abel differential equation with two nonlinear terms in order to demonstrate in as much detail as possible the computations necessary for a complete solution. We mention in our section on further developments that the basic transformation idea can be generalized to apply to differential equations of any order, to a system of ordinary differential equations without first differentially eliminating the multiple dependent variables, and even to partial differential equations.

math.RA↗

arXiv2008

Joint differential resolvents for pseudopolynomials

The existence of linear differential resolvents for z^alpha for any root z of an ordinary polynomial with coefficients in a given ordinary differential field has been established, where alpha is an indeterminate constant with respect to the derivation of the given field. In this paper we consider several alphas. We will call a finite sum of indeterminate powers of a variable v a pseudopolynomial in v. We will generalize the definition of a differential resolvent of a single polynomial for a single monomial z^alpha to the definition of a differential resolvent of several polynomials for a pseudopolynomial in the roots. We will also generalize the definition of a resolvent to have non-consecutive derivatives. We will show that the authors powersum formula may be used to compute this more general differential resolvent.

math.RA↗