Search results for "Differential equations"
showing 10 items of 169 documents
Oscillatory Behavior of Second-Order Nonlinear Neutral Differential Equations
2014
Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2014/143614 Open Access We study oscillatory behavior of solutions to a class of second-order nonlinear neutral differential equations under the assumptions that allow applications to differential equations with delayed and advanced arguments. New theorems do not need several restrictive assumptions required in related results reported in the literature. Several examples are provided to show that the results obtained are sharp even for second-order ordinary differential equations and improve related contributions to the subject.
Asymptotic Behavior of Higher-Order Quasilinear Neutral Differential Equations
2014
Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2014/395368 Open Access We study asymptotic behavior of solutions to a class of higher-order quasilinear neutral differential equations under the assumptions that allow applications to even- and odd-order differential equations with delayed and advanced arguments, as well as to functional differential equations with more complex arguments that may, for instance, alternate indefinitely between delayed and advanced types. New theorems extend a number of results reported in the literature. Illustrative examples are presented.
On the asymptotic behavior of solutions to a class of third-order nonlinear neutral differential equations
2020
Abstract By using comparison principles, we analyze the asymptotic behavior of solutions to a class of third-order nonlinear neutral differential equations. Due to less restrictive assumptions on the coefficients of the equation and on the deviating argument τ , our criteria improve a number of related results reported in the literature.
Periodic solutions of a class of non-autonomous second order differential equations with discontinuous right-hand side
2012
Abstract The main goal of this paper is to discuss the existence of periodic solutions of the second order equation: y ″ + η sgn ( y ) = α sin ( β t ) with ( η , α , β ) ∈ R 3 η > 0 . We analyze the dynamics of such an equation around the origin which is a typical singularity of non-smooth dynamical systems. The main results consist in exhibiting conditions on the existence of typical periodic solutions that appear generically in such systems. We emphasize that the mechanism employed here is applicable to many more systems. In fact this work fits into a general program for understanding the dynamics of non-autonomous differential equations with discontinuous right-hand sides.
A comparison analysis between unsymmetric and symmetric radial basis function collocation methods for the numerical solution of partial differential …
2002
Abstract In this article, we present a thorough numerical comparison between unsymmetric and symmetric radial basis function collocation methods for the numerical solution of boundary value problems for partial differential equations. A series of test examples was solved with these two schemes, different problems with different type of governing equations, and boundary conditions. Particular emphasis was paid to the ability of these schemes to solve the steady-state convection-diffusion equation at high values of the Peclet number. From the examples tested in this work, it was observed that the system of algebraic equations obtained with the symmetric method was in general simpler to solve …
Co-jumps and Markov Counting Systems in Random Environments
2020
Motivated by the analysis of multi-strain infectious disease data, we provide closed-form transition rates for continuous-time Markov chains that arise from subjecting Markov counting systems to correlated environmental noises. Noise correlation induces co-jumps or counts that occur simultaneously in several counting processes. Such co-jumps are necessary and sufficient for infinitesimal correlation between counting processes of the system. We analyzed such infinitesimal correlation for a specific infectious disease model by randomizing time of Kolmogorov’s Backward system of differential equations based on appropriate stochastic integrals.
OPKINE, a multipurpose program for kinetics
1991
The program OPKINE is presented for the study of reaction mechanisms and multicomponent analysis in dynamic conditions. This program is written in FORTRAN-77 for IBM 30/90 and VAX 8300 computers, and permits the simultaneous evaluation of both rate constants and initial reagent concentrations or, alternatively, rate constants and sensitivities. Up to 20 kinetic curves, with up to 400 points each, can be treated to evaluate up to 40 parameters. Integration of the system of differential equations is performed by means of the Runge–Kutta–Fehlberg method. OPKINE is provided with the Simplex, and modified versions of the Davidon–Fletcher–Powell and Gauss–Newton–Marquardt optimization methods. A …
Tractional Motion Machines: Tangent-Managing Planar Mechanisms as Analog Computers and Educational Artifacts
2012
Concrete and virtual machines play a central role in the both Unconventional Computing (machines as computers) and in Math Education (influence of artifacts on reaching/producing abstract thought). Here we will examine some fallouts in these fields for the Tractional Motion Machines, planar mechanisms based on some devices used to plot the solutions of differential equations by the management of the tangent since the late 17th century.
Fuzzy Control of Uncertain Nonlinear Systems with Numerical Techniques: A Survey
2019
This paper provides an overview of numerical methods in order to solve fuzzy equations (FEs). It focuses on different numerical methodologies to solve FEs, dual fuzzy equations (DFEs), fuzzy differential equations (FDEs) and partial fuzzy differential equations (PFDEs). The solutions which are produced by these equations are taken to be the controllers. This paper also analyzes the existence of the roots of FEs and some important implementation problems. Finally, several examples are reviewed with different methods.
The exact finite‐difference scheme for vector boundary‐value problems with piece‐wise constant coefficients
1998
We will consider the exact finite‐difference scheme for solving the system of differential equations of second order with piece‐wise constant coefficients. It is well‐known, that the presence of large parameters at first order derivatives or small parameters at second order derivatives in the system of hydrodynamics and magnetohydrodynamics (MHD) equations (large Reynolds, Hartmann and others numbers) causes additional difficulties for the applications of general classical numerical methods. Thus, important to work out special methods of solution, the so‐called uniform converging computational methods. This gives a basis for the development of special monotone finite vector‐difference schem…