Related papers: On a new closed formula for the solution of second…
Lie's linearizability criteria for scalar second-order ordinary differential equations had been extended to systems of second-order ordinary differential equations by using geometric methods. These methods not only yield the linearizing…
We use the Riccati equation method with other ones to establish new oscillation and interval oscillation criteria for linear matrix Hamiltonian systems. We investigate the oscillation problem for linear matrix Hamiltonian systems in a new…
We show a necessary and sufficient condition on the existence of finite order entire solutions of linear differential equations $$ f^{(n)}+a_{n-1}f^{(n-1)}+\cdots+a_1f'+a_0f=0,\eqno(+) $$ where $a_i$ are exponential sums for…
In this paper, we introduce a novel indefinite summation $\sum_{t} f(t)$ (or antidifference $\Delta ^{-1}f(t) $ ) formula for any given function $f$. We apply the indefinite summation formula to calculate a particular solution to a…
New solution method for the systems of linear equations in commutative integral domains is proposed. Its complexity is the same that the complexity of the matrix multiplication.
An alternative proof of Lie's approach for linearization of scalar second order ODEs is derived using the relationship between $\lambda$-symmetries and first integrals. This relation further leads to a new $\lambda$-symmetry linearization…
We consider a variational problem with boundary singularity and Dirichlet condition. We give a blow-up analysis for sequences of solutions of an equation with exponential nonlinearity. Also, we derive a compactness criterion under some…
In this article I present a fast and direct method for solving several types of linear finite difference equations (FDE) with constant coefficients. The method is based on a polynomial form of the translation operator and its inverse, and…
We show that, if an integer sequence is given by a linear recurrence of constant rational coefficients, then it can be represented as the difference of two arithmetic terms with exponentiation, which do not contain any irrational constant.…
The aim of this paper is to find the numerical solutions of the second order linear and nonlinear differential equations with Dirichlet, Neumann and Robin boundary conditions. We use the Bernoulli polynomials as linear combination to the…
In this note we show the the system of difference equations $$ x_{n+1}=\dfrac{ay_{n-2}x_{n-1}y_n+bx_{n-1}y_{n-2}+cy_{n-2}+d}{y_{n-2}x_{n-1}y_n},$$ $$y_{n+1}=\dfrac{ax_{n-2}y_{n-1}x_n+by_{n-1}x_{n-2}+cx_{n-2}+d}{x_{n-2}y_{n-1}x_n},$$ where…
A symmetric characteristic singular integral equation with two fixed singularities at the endpoints in the class of functions bounded at the ends is analyzed. It reduces to a vector Hilbert problem for a half-disc and then to a vector…
We present a new one parameter family of second derivative discontinuous solutions to the simplest scale invariant linear ordinary differential equation. We also point out how the construction could be extended to generate families of…
By using the method developed in the paper [G.Pantsulaia, G.Giorgadze, On some applications of infinite-dimensional cellular matrices, {\it Georg. Inter. J. Sci. Tech., Nova Science Publishers,} Volume 3, Issue 1 (2011), 107-129], it is…
In this short note we are presenting a method of finding particular solutions of nonhomegeneous linear equations. This approach is different from methods of undetermined coefficients or variation of parameters presented in virtually every…
We consider continuous linear programs over a continuous finite time horizon $T$, with a constant coefficient matrix, linear right hand side functions and linear cost coefficient functions, where we search for optimal solutions in the space…
Lie group analysis of the difference equations of the form \begin{align*} x_{n+1} =\frac{x_{n-4}x_{n-3}}{x_{n}(a_n +b_nx_{n-4}x_{n-3}x_{n-2}x_{n-1})}, \end{align*} where $a_n$ and $b_n$ are real sequences, is performed and non-trivial…
In this paper, using the similarity method, we construct particular solutions with singularities for degenerate high-order equations. The considered equations have singularities of the first and second kind. Particular solutions are…
In this paper, we explore a variety of series involving the central binomial coefficients, highlighting their structural properties and connections to other mathematical objects. Specifically, we derive new closed-form representations and…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…