Here, the solution in one, two and three dimensional for the Volterra–Fredholm integral equation of the first kind is obtained in the space L2ðXÞ C1⁄20; T , T < 1. Using a numerical method the integral equation of Volterra–Fredholm becomes a linear system of Fredholm integral equation when that the kernel of Fredholm integral takes a logarithmic form, Carleman function, generalized potential fu...

In this article, we apply the operational matrix to find the numerical solution of two- dimensional nonlinear Volterra integro-differential equation (2DNVIDE). Form this prospect, two-dimensional shifted Legendre functions (2DSLFs) has been presented for integration, product as well as differentiation. This method converts 2DNVIDE to an algebraic system of equations, so the numerical solution o...

A general system of high-order differential equations describing complex dynamics of replicating biomolecules is given. Symmetry relations and coordinate transformations of general replication systems leading to topologically equivalent systems are derived. Three chaotic attractors observed in Lotka-Volterra equations of dimension n = 3 are shown to represent three cross-sections of one and the...

Volterra difference equations arise in the mathematical modeling of some real phenomena, and also in numerical schemes for solving differential and integral equations (cf. [7, 8] and the references therein). One of the basic methods in the theory of stability and boundedness of Volterra difference equations is the direct Lyapunov method (see [1, 3, 4] and the references therein). But finding th...

The dynamics of n-dimensional Lotka–Volterra equations having an invariant hyperplane is investigated herein. There exists a fundamental difference between the evenand the odd-dimensional case. For even dimensions the dynamics are generated by a Hamiltonian system with respect to an appropriately chosen Poisson structure. For odd dimensions the dynamics are Hamiltonian if there is a continuum o...

We give asymptotic classification of the positive solutions of a class of two-dimensional nonlinear Volterra integro-differential equations. Also, we furnish necessary and conditions for the existence of such positive solutions.

In this paper, the two-dimensional triangular orthogonal functions (2D-TFs) are applied for solving a class of nonlinear two-dimensional Volterra integral equations. 2D-TFs method transforms these integral equations into a system of linear algebraic equations. The high accuracy of this method is verified through a numerical example and comparison of the results with the other numerical methods.

This paper aims to contribute to research on the question of the stabilization or destabilization of a deterministic dynamical system (differential equation, partial differential equation, or functional differential equation) by a noise perturbation, and in particular, perturbations which transform the differential equation (or FDE) to one of Itô-type. Mao has written an interesting paper [9] d...

This paper introduces a new methods for three-dimensional(3D) ocean bathymetry reconstruction using Airborne TOPSAR Synthetic Aperture data. The new method is based on integration between Fuzzy B-spline and Volterra algorithm. Volterra algorithm is used to simulate the ocean surface current from TOPSAR data. Then, ocean surface current information used as input for continuity equation to estima...