Related papers: Apparent Singularities of D-finite Systems
The method of this paper is my original creation. A new method for solving linear differential equations is proposed in this paper. The important conclusion of this paper is that arbitrary order linear ordinary differential equations with…
We provide a characterization for a periodic system of generalized Sylvester and conjugate-Sylvester equations, with at most one generalized conjugate-Sylvester equation, to have a unique solution when all coefficient matrices are square…
We develop a new theory for treating boundary problems for linear ordinary differential equations whose fundamental system may have a singularity at one of the two endpoints of the given interval. Our treatment follows an algebraic…
Closed-form differential equations, including partial differential equations and higher-order ordinary differential equations, are one of the most important tools used by scientists to model and better understand natural phenomena.…
We describe a theory of finite sets, and investigate the analogue of Dedekind's theory of natural number systems (simply infinite systems) in this theory. Unlike the infinitary case, in our theory, natural number systems come in differing…
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…
General solutions of nonlinear ordinary differential equations (ODEs) are in general difficult to find although powerful integrability techniques exist in the literature for this purpose. It has been shown that in some scalar cases…
A family of asymptotic solutions at infinity for the system of ordinary differential equations is considered. Existence of exact solutions which have these asymptotics is proved.
In the classification of real singularities by Arnold et al. (1985), normal forms, as representatives of equivalence classes under right equivalence, are not always uniquely determined. We describe the complete structure of the equivalence…
Let $A$ be a subvariety of affine space $\mathbb{A}^n$ whose irreducible components are $d$-dimensional linear or affine subspaces of $\mathbb{A}^n$. Denote by $D(A)\subset\mathbb{N}^n$ the set of exponents of standard monomials of $A$. We…
This paper exhibits a very simple formula for a particular solution of a linear ordinary differential equation with constant real coefficients, P(d/dt)x = f, f a function given by a linear combination of polynomials, trigonometrical and…
In this paper we presents further developments regarding the enrichment of the basic Theory of Order Completion. In particular, spaces of generalized functions are constructed that contain generalized solutions to all systems of continuous,…
An infinite set is orbit-finite if, up to permutations of the underlying structure of atoms, it has only finitely many elements. We study a generalisation of linear programming where constraints are expressed by an orbit-finite system of…
System of semilinear ordinary differential equation and fractional differential equation of distributed order is investigated and solved in a mild and classical sense. Such a system arises as a distributed derivative model of…
We examine the notion of anticonfinement and the role it has to play in the singularity analysis of discrete systems. A singularity is said to be anticonfined if singular values continue to arise indefinitely for the forward and backward…
We classify the singularities of a surface ruled by conics: they are rational double points of type $A_n$ or $D_n$. This is proved by showing that they arise from a precise series of blow-ups of a suitable surface geometrically ruled by…
New problem is considered that is to find nonlinear differential equations with special solutions. Method is presented to construct nonlinear ordinary differential equations with exact solution. Crucial step to the method is the assumption…
In this paper, we study the algebraic, rational and formal Puiseux series solutions of certain type of systems of autonomous ordinary differential equations. More precisely, we deal with systems which associated algebraic set is of…
We give an overview of invariants of algebraic singularities over perfect fields. We then show how they lead to a synthetic proof of embedded resolution of singularities of 2-dimensional schemes.
The linear complete differential resultant of a finite set of linear ordinary differential polynomials is defined. We study the computation by linear complete differential resultants of the implicit equation of a system of $n$ linear…