9 citations · 18 across the 14 of their papers we have counts for
4 papers · 1 filter
Rational Solutions of Parametric First-Order Algebraic Differential Equations
Sebastian Falkensteiner, Rafael Sendra
In this paper, we give an algorithm for finding general rational solutions of a given first-order ODE with parametric coefficients that occur rationally. We present an analysis, co…
On real and observable rational realizations of input-output equations
Sebastian Falkensteiner, Dmitrii Pavlov, Rafael Sendra
Given a single (differential-algebraic) input-output equation, we present a method for finding different representations of the associated system in the form of rational realizatio…
On Existence and Uniqueness of Formal Power Series Solutions of Algebraic Ordinary Differential Equations
Sebastian Falkensteiner, Yi Zhang, Thieu N. Vo
Given an algebraic ordinary differential equation (AODE), we propose a computational method to determine when a truncated power series can be extended to a formal power series solu…
Solving First Order Autonomous Algebraic Ordinary Differential Equations by Places
Sebastian Falkensteiner, J. Rafael Sendra
Given a first-order autonomous algebraic ordinary differential equation, we present a method for computing formal power series solutions by means of places. We provide an algorithm…