Related papers: The Dynamical Systems Method for solving nonlinear…
In this paper, we approach the problem of finding the zeros of the sum of a maximally monotone operator and a monotone and Lipschitz continuous one in a real Hilbert space via an implicit forward-backward-forward dynamical system with…
First order optimization algorithms play a major role in large scale machine learning. A new class of methods, called adaptive algorithms, were recently introduced to adjust iteratively the learning rate for each coordinate. Despite great…
In this paper, we mainly establish the existence of at least three non-trivial solutions for a class of nonhomogeneous quasilinear elliptic systems with Dirichlet boundary value or Neumann boundary value in a bounded domain…
The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems…
We present a new solution for fundamental problems in nonlinear dynamical systems: finding, verifying, and stabilizing cycles. The solution we propose consists of a new control method based on mixing previous states of the system (or the…
For a large family of nonautonomous scalar-delayed differential equations used in population dynamics, some criteria for permanence are given, as well as explicit upper and lower bounds for the asymptotic behavior of solutions. The method…
We study the dynamics of four families of methods obtained with a weight function from a convex combination of Newton's method and a Newton-Halley type method on polynomials with two roots. We find the analytical expressions for the fixed…
Direct solution of simultaneous linear equations is regarded to be slow for large systems of equations and requires special treatment to avoid numerical instability. A new method is proposed that addresses the numerical instability without…
We review some of the recent developments and prove new results concerning frames and Bessel systems generated by iterations of the form $\{A^ng: g\in G,\, n=0,1,2,\dots \}$, where $A$ is a bounded linear operators on a separable complex…
We study systems of nonlinear partial differential equations of parabolic type, in which the elliptic operator is replaced by the first order divergence operator acting on a flux function, which is related to the spatial gradient of the…
A decomposition principle for nonlinear dynamic compartmental systems is introduced in the present paper. This theory is based on the mutually exclusive and exhaustive, analytical and dynamic, novel system and subsystem partitioning…
We construct two rational approximate solutions to the Thomas-Fermi (TF) nonlinear differential equation. These expressions follow from an application of the principle of dynamic consistency. In addition to examining differences in the…
In this paper we consider the model semilinear Neumann system $$\left\{ \begin{array}{lll} -\Delta u+a(x)u=\lambda c(x) F_u(u,v)& {\rm in} & \Omega,\\ -\Delta v+b(x)v=\lambda c(x) F_v(u,v)& {\rm in} & \Omega,\\ \frac{\partial u}{\partial…
In this paper, we propose and analyze a third-order dynamical system for solving a generalized inverse mixed variational inequality problem in a Hilbert space H. We establish the existence and uniqueness of the trajectories generated by the…
Classical and nonclassical symmetries of the nonlinear heat equation $$u_t=u_{xx}+f(u),\eqno(1)$$ are considered. The method of differential Gr\"obner bases is used both to find the conditions on $f(u)$ under which symmetries other than the…
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…
Numerical investigations of partial differential equations with hysteresis have largely focused on simulations, leaving numerical error analysis unexplored and relying mainly on derivative-free nonlinear solvers. This work establishes…
The following document presents a possible solution and a brief stability analysis for a nonlinear system, which is obtained by studying the possibility of building a hybrid solar receiver; It is necessary to mention that the solution of…
Methods of dynamical systems have been used to study homogeneous and isotropic cosmological models with a varying speed of light (VSL). We propose two methods of reduction of dynamics to the form of planar Hamiltonian dynamical systems for…
Modal synthesis methods are a long-standing approach for modelling distributed musical systems. In some cases extensions are possible in order to handle geometric nonlinearities. One such case is the high-amplitude vibration of a string,…