in this paper the periodic solutions of fourth order delay differential equation of the form $ddddot{x}(t)+adddot{x}(t)+f(ddot{x}(t-tau(t)))+g(dot{x}(t-tau(t)))+h({x}(t-tau(t)))=p(t)$  is investigated. some new positive periodic criteria are given.

in this paper, we prove the existence of the solution for boundary value prob-lem(bvp) of fractional dierential equations of order q 2 (2; 3]. the kras-noselskii's xed point theorem is applied to establish the results. in addition,we give an detailed example to demonstrate the main result.

Metastable dynamics, which qualitatively refers to physical processes that involve an extremely slow approach to their nal equilibrium states, is often associated with singularly perturbed convection-di usion-reaction equations. A problem exhibits metastable behavior when the approach to equilibrium occurs on a time-scale of order O(eC" ), where C > 0 and " is the singular perturbation paramete...

Higher-order intergrid transfer operators used within cell-centered multigrid can improve the convergence properties of the multigrid method compared to low-order operators. In this thesis those operators are analyzed and incorporated into the LSE (linear systems of equation) module of the waLBerla software framework. The aim is to provide a solver for Poisson and Poisson-Boltzmann partial di e...

Abstract. We present a new tunably-accurate Laguerre Petrov-Galerkin spectral method for solving linear multi-term fractional initial value problems with derivative orders at most one and constant coe cients on the half line. Our method results in a matrix equation of special structure which can be solved in O(N logN) operations. We also take advantage of recurrence relations for the generalize...

in this work, we conduct a comparative study among the combine laplace transform and modied adomian decomposition method (lmadm) and two traditional methods for an analytic and approximate treatment of special type of nonlinear volterra integro-differential equations of the second kind. the nonlinear part of integro-differential is approximated by adomian polynomials, and the equation is red...

Since the advent of Taylor Series, polynomial methods have been used to solve di↵erential equations and learn the properties of di↵erential equations. There are many polynomial methods for solving di↵erential equations and understanding dynamical systems. For example, Taylor polynomials, Chebyshev Polynomials and Adomian Polynomials are used to generate approximate solutions. Automatic di↵erent...

The problem of learning qualitative models of physical systems from observations of its behaviour has been addressed by several researchers in recent years. Most current techniques limit themselves to learning a single qualitative di erential equation to model the entire system. However, many systems have several qualitative differential equations underlying them. In this paper, we present an a...

In this paper, decision{feedback di erential detection (DF{DD) ofM{ary di erential phase{shift keying (MDPSK) signals, which has been introduced previously for the additive white Gaussian noise (AWGN) channel by Leib et al. [1] and Edbauer [2], is extended to at Rayleigh fading channels. The DF{DD metric is derived from the multiple{symbol detection (MSD) metric and for error{free feedback an e...

The Poisson-Boltzmann (PB) equation describes the electrostatic potential of a biomolecular system composed by a molecule in a solvent. The electrostatic potential is involved in biomolecular models which are used in molecular simulation. In consequence, nding an e cient method to simulate the numerical solution of PB equation is very useful. As a rst step, we establish in this paper a probabil...