The main goal of the present work is to investigate effect noise in some neural fields, used simulate working memory processes. underlying mathematical model a stochastic integro-differential equation. In order approximate this equation we apply numerical scheme which uses Galerkin method for space discretization. way obtain system differential equations, are then approximated two different way...

In this paper , numerical solotion of Abel's integral equationby using the Taylor expanssion of the unknown functionvia collection method based on Sinc is considered...

Abstract This paper presents an appropriate numerical method to solve nonlinear Fredholm integro-differential equations with time delay. Its approach is based on the Taylor expansion. This method converts the integro-differential equation and the given conditions into the matrix equation which corresponds to a system of nonlinear algebraic equations with unknown Taylor expansion coefficients, s...

Formulated is a new systematic method for obtaining higher order corrections in numerical simulation of stochastic differential equations (SDEs), i.e., Langevin equations. Random walk step algorithms within a given order of finite ∆t, are obtained so as to reproduce within that order a corresponding transition density of the Fokker-Planck equations, in the weak Taylor approximation scheme [1]. ...

This article proposes an optimal method for approximate answer of stochastic Ito-Voltrra integral equations, via rationalized Haar functions and their stochastic operational matrix of integration. Stochastic Ito-voltreea integral equation is reduced to a system of linear equations. This scheme is applied for some examples. The results show the efficiency and accuracy of the method.

the distribution pattern of pest population is one of the factors not only effects on sampling program and data analysis method, but also can be used to measure the density of pests and their natural enemies. thus, the spatial distribution pattern of the pea aphid, acyrthosiphon pisum harris (hem.: aphididae) and its two major predators, hippodamia variegata goeze (col.: coccinellidae) and cocc...

In the present paper the Renormalization Group (RG) method is adopted as a tool for a constructive analysis of the properties of the Frobenius-Perron Operator. The renormalization group reduction of a generic symplectic map in the case, where the unperturbed rotation frequency of the map is far from structural resonances driven by the kick perturbation has been performed in detail. It is furthe...

We consider second order parabolic equations with coefficients that vary both in space and in time (non-autonomous). We derive closedform approximations to the associated fundamental solution by extending the Dyson-Taylor commutator method that we recently established for autonomous equations. We establish error bounds in Sobolev spaces and show that by including enough terms, our approximation...

Deep neural networks are powerful parametric models that can be trained efficiently using the backpropagation algorithm. Stochastic neural networks combine the power of large parametric functions with that of graphical models, which makes it possible to learn very complex distributions. However, as backpropagation is not directly applicable to stochastic networks that include discrete sampling ...

Quasi-Newton methods for numerical optimization exploit quadratic Taylor polynomial models of the objective function. Trust regions are widely used to ensure the global convergence of these methods. Analogously, response surface methods for stochastic optimization exploit linear and quadratic regression models of the objective function. Ridge analysis is widely used to safeguard the optimizatio...