We study oscillatory behavior of a class of second-order neutral di¤erential equations relating oscillation of these equations to existence of positive solutions to associated first-order functional di¤erential inequalities. Our assumptions allow applications to di¤erential equations with both delayed and advanced arguments, and not only. New theorems complement and improve a number of results ...

in this study, a new and ecient approach is presented for numerical solution offredholm integro-dierential equations (fides) of the second kind on unbounded domainwith degenerate kernel based on operational matrices with respect to generalized laguerrepolynomials(glps). properties of these polynomials and operational matrices of integration,dierentiation are introduced and are ultilized to r...

Fractional calculus has been used to model physical and engineering processes that are found to be best described by fractional diff<span style="font-family: NimbusRomNo...

Fractional calculus is a natural extension of the integer order calculus and recently, a large number of applied problems have been formulated on fractional di¤erential equations. Analytical solution of many applications, where the fractional di¤erential equations appear, cannot be established. Therefore, cubic polynomial spline function is considered to …nd approximate solution for fractional ...

The e ciency of numerically solving time-dependent partial di erential equations on parallel computers can be greatly improved by computing the solution on many time-levels simultaneously. The theoretical properties of one such method, namely the discrete-time multigrid waveform relaxation method, are investigated for systems of ordinary di erential equations obtained by spatial nite element di...

We present an extension of the lambda-calculus with di erential constructions. We state and prove some basic results (con uence, strong normalization in the typed case), and also a theorem relating the usual Taylor series of analysis to the linear head reduction of lambda-calculus.

We present an overview of intrinsic integration schemes for diierential equations evolving on manifolds, paying particular attention to homogeneous spaces. Various examples of applications are introduced , showing the generality of the methods. Finally we discuss abstract Runge{Kutta methods. We argue that homogeneous spaces are the natural structures for the study and the analysis of these met...

in this paper a numerical method for solving forth order fuzzy dierentialequations under generalized differentiability is proposed. this method is basedon the interpolating a solution by piecewise polynomial of degree 8 in the rangeof solution . we investigate the existence and uniqueness of solutions. finally anumerical example is presented to illustrate the accuracy of the new technique.

We derive a rst-order approximation of the density of maximum entropy for a continuous 1-D random variable, given a number of simple constraints. This results in a density expansion which is somewhat similar to the classical polynomial density expansions by Gram-Charlier and Edgeworth. Using this approximation of density, an approximation of 1-D diierential entropy is derived. The approximation...