This paper extends the results of synaptically generated wave propagation through a network of connected excitatory neurons to a continuous model, defined by a Fredholm Volterra integro-differential equation (FVIDE), which includes memory effects of the past in the propagation. Stochastic approximation and numerical simulations are discussed. 2006 Elsevier Inc. All rights reserved.

In this paper, a method based on the Tau method with arbitrary bases is developed to find the numerical solution of Fredholm integro-differential equations; the differential part appearing in the equation is replaced by its operational Tau representation. Some numerical results are given to demonstrate the superior performance of the Tau method, particularly, with the Chebyshev and Legendre bas...

Abstract: In this paper, a numerical method to solve nonlinear Fredholm integral equations of second kind is proposed and some numerical notes about this method are addressed. The method utilizes Chebyshev wavelets constructed on the unit interval as a basis in the Galerkin method. This approach reduces this type of integral equation to solve a nonlinear system of algebraic equation. The method...

An attempt is made to develop approximate method get solution of system linear Fredholm fractional integro-differential equations using Least squares and Lauguerre polynomial method. The reduced a polynomials. implemented obtain the equations. solutions are simulated Scilab.

We study the parametrized Hamiltonian action functional for finitedimensional families of Hamiltonians. We show that the linearized operator for the L2-gradient lines is Fredholm and surjective, for a generic choice of Hamiltonian and almost complex structure. We also establish the Fredholm property and transversality for generic S1-invariant families of Hamiltonians and almost complex structur...

The present paper is devoted to the development of a kind of spectral meshless radial point interpolation (SMRPI) technique in order to obtain a reliable approximate solution for buckling of nano-actuators subject to different nonlinear forces. To end this aim, a general type of the governing equation for nano-actuators, containing integro-differential terms and nonlinear forces is considered. ...

The Tau method, produces approximate polynomial solution of differential, integral and integro-differential equations (see [E.l,Ortiz, The Tau method, SIAM J. Numer. Anal. 6 (3) (1969) 480–492; E.l. Ortiz, H. Samara, An operational approach to the Tau method for the numerical solution of non-linear differential equations, Computing 27 (1981) 15–25; S.M. Hosseini, S. Shahmorad, A matrix formulat...

The homotopy analysis method [1, 2], is developed to search the accurate asymptotic solutions of nonlinear problems. This technique has been successfully applied to many nonlinear problems such as the viscous flows of non-Newtonian fluids [3, 4], the Korteweg-de Vries-type equations [5, 6], nonlinear heat transfer [7, 8], finance problems [9, 10], Riemann problems related to nonlinear shallow w...

We present a relatively new and very efficient method to find approximate analytical solutions for general class of nonlinear fractional Volterra Fredholm integro-differential equations. The test problems included the comparison with previous results by other methods clearly illustrate simplicity accuracy method.

In this study, the numerical solution of Fredholm integro–differential equation is discussed in a reproducing kernel Hilbert space. A reproducing kernel Hilbert space is constructed, in which the initial condition of the problem is satisfied. The exact solution u x ð Þ is represented in the form of series in the space W 2 2 ½a; bŠ. In the mean time, the n-term approxima te solution u n ðxÞ is o...