Related papers: Interesting system of $3$ first-order recursions

In present paper we propose seemingly new method for finding solutions of some types of nonlinear PDEs in closed form. The method is based on decomposition of nonlinear operators on sequence of operators of lower orders. It is shown that…

Liveness properties are traditionally proven using a ranking function that maps system states to some well-founded set. Carrying out such proofs in first-order logic enables automation by SMT solvers. However, reasoning about many natural…

This paper deals with a problem from discrete-time robust control which requires the solution of constraints over the reals that contain both universal and existential quantifiers. For solving this problem we formulate it as a program in a…

This work considers special types of interval linear systems - overdetermined systems. Simply said these systems have more equations than variables. The solution set of an interval linear system is a collection of all solutions of all…

We prove the global classical solvability of initial-boundary problems for semilinear first-order hyperbolic systems subjected to local and nonlocal nonlinear boundary conditions. We also establish lower bounds for the order of nonlinearity…

We report a class of symmetry-intergable third-order evolution equations in 1+1 dimensions under the condition that the equations admit a second-order recursion operator that contains an adjoint symmetry (integrating factor) of order six.…

This paper applies He's new amplitude-frequency relationship recently established by Ji-Huan He (Int J Appl Comput Math 3 1557-1560, 2017) to study periodic solutions of strongly nonlinear systems with odd nonlinearities. Some examples are…

In this paper, we introduce and study a class of resolvent dynamical systems to investigate some inertial proximal methods for solving mixed variational inequalities. These proposed methods along with their discretizations and derived rates…

In order to solve an initial value problem by the variational iteration method, a sequence of functions is produced which converges to the solution under some suitable conditions. In the nonlinear case, after a few iterations the terms of…

Iterative methods based on matrix splittings are useful in solving large sparse linear systems. In this direction, proper splittings and its several extensions are used to deal with singular and rectangular linear systems. In this article,…

Let t[n] be a sequence that satisfies a first order homogeneous recurrence t[n] = Q[n]*t[n-1], where Q is a polynomial with integer coefficients. The asymptotic behavior of the p-adic valuation of t[n] is described under the assumption that…

The aim of this paper is to investigate the dynamics of a higher order system of rational difference equations. Our concentration is on boundedness character, the oscillatory, the existence of unbounded solutions and the global behavior of…

We consider a linear second order parabolic system with a third order dispersion term. This type of system arises when considering a nonlinear model equation describing the motion of a vortex filament with axial flow immersed in an…

It was recently conjectured that every component of a discrete-time rational dynamical system is a solution to an algebraic difference equation that is linear in its highest-shift term (a quasi-linear equation). We prove that the conjecture…

In this paper, we give an algorithm for finding general rational solutions of a given first-order ODE with parametric coefficients that occur rationally. We present an analysis, complete modulo Hilbert's irreducibility problem, of the…

In this article, we prove an existence of solutions for a non-local boundary value problem with nonlinearity in a nonlocal condition. Our method is based upon the Mawhin's coincidence theory.

In this paper the local order of convergence used in iterative methods to solve nonlinear systems of equations is revisited, where shorter alternative analytic proofs of the order based on developments of multilineal functions are shown.…

Here we present a new approach to deal with first order ordinary differential equations (1ODEs), presenting functions. This method is an alternative to the one we have presented in [1]. In [2], we have establish the theoretical background…

We consider asynchronous versions of the first and second order Richardson methods for solving linear systems of equations. These methods depend on parameters whose values are chosen a priori. We explore the parameter values that can be…

The paper deals with the decoupling problem of general quasilinear first order systems in two independent variables. We consider either the case of homogeneous and autonomous systems or the one of nonhomogeneous and/or nonautonomous…