Related papers: Linear differential systems over the quaternion sk…
In this paper we presents an algorithm for finding a solution of the linear nonhomogeneous quaternionic-valued differential equations. Moveover, several examples shows the feasibility of our algorithm.
In this paper we develop a theory of linear differential systems analogous to the classical one for ODEs, including the obtaining of fundamental matrices, the development of a variation of parameters formula and the expression of the…
This book is mainly an exposition of the author's works and his joint works with his former students on explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic…
Solving linear systems of equations plays a fundamental role in numerous computational problems from different fields of science. The widespread use of numerical methods to solve these systems motivates investigating the feasibility of…
Generalizing the main result of [Aparicio-Monforte A., Compoint E., Weil J.-A., J. Pure Appl. Algebra 217 (2013), 1504-1516], we prove that a linear differential system is in reduced form in the sense of Kolchin and Kovacic if and only if…
We study the autonomous systems of quadratic differential equations of the form $\dot{x}_i(t)=\mathbf{x}(t)^T \mathbf{A}_i \mathbf{x}(t) + \mathbf{v}_i^T \mathbf{x}(t)$ with $\mathbf{x}(t) = (x_1(t),x_2(t),\dots,x_i(t),\dots)$ which, in…
This is an introduction to the theory of disconjugacy for a second order linear differential equation. We give new proofs of some of basic results and obtain new sufficient conditions for disconjugacy (in particular, on the whole real…
The general framework for integrable discrete systems on R in particular containing lattice soliton systems and their q-deformed analogues is presented. The concept of regular grain structures on R, generated by discrete one-parameter…
A class of fourth--order neutral type difference equations with quasidifferences and deviating arguments is considered. Our approach is based on studying the considered equation as a system of a four--dimensional difference system. The…
The paper introduces and studies differentially positive systems, that is, systems whose linearization along an arbitrary trajectory is positive. A generalization of Perron Frobenius theory is developed in this differential framework to…
In this paper, we present methods to simplify reducible linear differential systems before solving. Classical integrals appear naturally as solutions of such systems. We will illustrate the methods developed in a previous paper on several…
New real structure-preserving decompositions are introduced to develop fast and robust algorithms for the (right) eigenproblem of general quaternion matrices. Under the orthogonally JRS-symplectic transformations, the Francis JRS-QR step…
In this paper we generalize the involutive methods and algorithms devised for polynomial ideals to differential ones generated by a finite set of linear differential polynomials in the differential polynomial ring over a zero characteristic…
In this paper, we propose the global quaternion full orthogonalization (Gl-QFOM) and global quaternion generalized minimum residual (Gl-QGMRES) methods, which are built upon global orthogonal and oblique projections onto a quaternion matrix…
Invariant linearization criteria of square systems of second-order quadratically semi-linear ordinary differential equations (ODEs) that can be represented as geodesic equations are extended to square systems of ODEs cubically nonlinear in…
This paper is a summary of the theory of discrete embeddings introduced in [5]. A discrete embedding is an algebraic procedure associating a numerical scheme to a given ordinary differential equation. Lagrangian systems possess a…
The spectral method for building first integrals of ordinary linear differential systems is elaborated. Using this method, we obtain bases of first integrals for linear differential systems with constant coefficients, for linear…
We propose new algorithms for the computation of the first N terms of a vector (resp. a basis) of power series solutions of a linear system of differential equations at an ordinary point, using a number of arithmetic operations which is…
We use a recently found method to characterise all the invertible fourth-order difference equations linear in the extremal values based on the existence of a discrete Lagrangian. We also give some result on the integrability properties of…
Employing the Fast Fourier Transform we propose a ready-to-use solution to circulant real linear systems of equations, particularly useful when a broader theoretical analysis is involved. We also show that strict diagonal dominance of the…