We discuss the construction and estimates of the Green and Poisson functions associated with a parabolic second order integro-differential operator with Wentzell boundary conditions.

A new class of stochastic resonator (SRT) and Stochastic Resonance (SR) phenomena are described. The new SRT consist of a classical SRT, one or more time derivative circuits and the same number of time integrators. The incoming signal with additive noise is first time derivated, then passes through the classical SRT and finally it is time integrated. The resulting SR phenomena show a well defin...

We consider an approximation scheme for integro-partial differential equations which arise in the theory of linear viscoelas-ticity. This scheme is based on a modiication (to account for the singular kernel) of certain averaging type approximation methods for delay equations. We use this scheme to investigate the eeects of a history parameter (the delay length) on the behavior of the eigenvalue...

We consider the following partial integro-differential equation (Allen–Cahn equation with memory): φt = ∫ t 0 a(t − t ′)[ ∆φ + f (φ)+ h](t ′) dt ′, where is a small parameter, h a constant, f (φ) the negative derivative of a double well potential and the kernel a is a piecewise continuous, differentiable at the origin, scalar-valued function on (0,∞). The prototype kernels are exponentially dec...

in this letter, the numerical scheme of nonlinear volterra-fredholm integro-differential equations is proposed in a reproducing kernel hilbert space (rkhs). the method is constructed based on the reproducing kernel properties in which the initial condition of the problem is satised. the nonlinear terms are replaced by its taylor series. in this technique, the nonlinear volterra-fredholm integr...

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...

in this article we have considered a non-standard finite difference method for the solution of second order  fredholm integro differential equation type initial value problems. the non-standard finite difference method and the composite trapezoidal quadrature method is used to transform the fredholm integro-differential equation into a system of equations. we have also developed a numerical met...

In this study‎, ‎an efficient method is presented for solving infinite boundary integro-differential equations (IBI-DE) of the second kind with degenerate kernel in terms of Laguerre polynomials‎. ‎Properties of these polynomials and operational matrix of integration are first presented‎. ‎These properties are then used to transform the integral equation to a matrix equation which corresponds t...