ABSTRACT In this paper we first analyze the problem of equivalence of differential, functional and difference equations and give methods to move between them. We also introduce functional networks, a powerful alternative to neural networks, which allow neural functions to be different, multidimensional, multi-argument and constrained by link connections, and use them for predicting values of ma...

The prevalent model to describe propagation of neural membrane voltage responses to ion currents is the cable equation. The cable equation is a parabolic-type partial differential equation, which is frequently studied with the use of compartmental models. This paper explores other solution techniques for this type of partial differential equation, specifically the finite difference and finite e...

rolling-based seismic isolation systems, in which rollers of circular or non-circular section are used, are less expensive and easier to manufacture. however, this type of isolation suffers from either lack of restoring or re-centering capability, or weakness against uplift forces. to resolve the first shortcoming the use of elliptical as well as pillow-shape rolling parts has been suggested, a...

the edge detour index polynomials were recently introduced for computing theedge detour indices. in this paper we nd relations among edge detour polynomials for the2-dimensional graph of tuc4c8(s) in a euclidean plane and tuc4c8(s) nanotorus.

Purpose: To investigate the Lie groups of transformations (symmetries) approximately admitted by a finite difference discretization of a nonlinear advection equation on an unstructured mesh. Method: A recently developed technique of " approximate group analysis " is applied to a differential approximation (otherwise referred to as an equivalent differential equation) corresponding to the above ...

Differential–difference equation; Collocation points; Polynomial solutions Abstract This paper contributes a new matrix method for solving systems of high-order linear differential–difference equations with variable coefficients under given initial conditions. On the basis of the presented approach, the matrix forms of the Euler polynomials and their derivatives are constructed, and then by sub...