Related papers: Numerical solution of several second-order ordinar…
A new problem is studied, the concept of exactness of a second order nonlinear ordinary differential equations is established. A method is constructed to reduce this class into a first order equations. If the second order equation is not…
Second order linear non-autonomous differential equations with negative stiffness are considered. Using Chetaev-like (Lyapunov-like) functions, necessary (sufficient) conditions are found for the solutions to be bounded for all initial…
We exhibit an alternative method for solving inhomogeneous second--order linear ordinary dynamic equations on time scales, based on reduction of order rather than variation of parameters. Our form extends recent (and long-standing) analysis…
A theorem providing necessary conditions enabling one to map a nonlinear system of first order partial differential equations to an equivalent first order autonomous and homogeneous quasilinear system is given. The reduction to quasilinear…
In this paper, a quantum dot mathematical model based on a two-dimensional Schr\"odinger equation assuming the 1/r inter-electronic potential is revisited. Generally, it is argued that the solutions of this model obtained by solving a…
A new, second-order solution in curvilinear coordinates is introduced for the relative motion of two spacecraft on eccentric orbits. The second-order equations for unperturbed orbits are derived in spherical coordinates with true anomaly as…
In this paper we consider a class of fourth order nonlinear integro-differential equations with Navier boundary conditions. By the reduction of the problem to operator equation we establish the existence and uniqueness of solution and…
In this paper, we introduce an iterative numerical method to solve systems of nonlinear equations. The third-order convergence of this method is analyzed. Several examples are given to illustrate the efficiency of the proposed method.
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
Exact solutions of some popular nonlinear ordinary differential equations are analyzed taking their Laurent series into account. Using the Laurent series for solutions of nonlinear ordinary differential equations we discuss the nature of…
In this paper, we present a method to identify integrable complex nonlinear oscillator systems and construct their solutions. For this purpose, we introduce two types of nonlocal transformations which relate specific classes of nonlinear…
We study a probabilistic numerical method for the solution of both boundary and initial value problems that returns a joint Gaussian process posterior over the solution. Such methods have concrete value in the statistics on Riemannian…
This article deals with the second order linear differential equations with entire coefficients. We prove some results involving conditions on coefficients so that the order of growth of every non-trivial solution is infinite.
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…
In this work we introduce and analyze a new multiscale method for strongly nonlinear monotone equations in the spirit of the Localized Orthogonal Decomposition. A problem-adapted multiscale space is constructed by solving linear local…
In the first part of planned series of papers the formal general solutions to selection of 80 examples of different types of second order nonlinear PDEs in two independent variables with constant parameters are given. The main goal here is…
The article presents a matrix differential operator and a pseudoinverse matrix differential operator for finding a particular solution to nonhomogeneous linear ordinary differential equations (ODE) with constant coefficients with special…
Olver and Rosenau studied group-invariant solutions of (generally nonlinear) partial differential equations through the imposition of a side condition. We apply a similar idea to the special case of finite-dimensional Hamiltonian systems,…
In this work, we introduce a novel numerical method for solving initial value problems associated with a given differential. Our approach utilizes a spline approximation of the theoretical solution alongside the integral formulation of the…
In this paper, we have considered second order non-homogeneous linear differential equations having entire coefficients. We have established conditions ensuring non-existence of finite order solution of such type of differential equations.