相关论文: Numerical solution of locally loaded Volterra inte…

We prove the existence of weak solutions for distribution-dependent stochastic Volterra equations under linear growth and continuity conditions on the coefficients and mild regularity assumptions on the kernels, including singular kernels.…

By means of two fractional order integral inequalities we investigate the existence and uniqueness of the solutions of the fractional nonlinear Volterra integral equation and a fractional nonlinear integrodifferential equation in Banach…

In this work we show how auxiliary variables can be used to give an efficient method involving symbolic manipulation and Picard iteration for approximating solutions of certain Volterra integral equations.

Some corrections are made in our article, which was published in Appl. Anal. Optim. Vol. 3 (2019), No. 1, 103--127. These corrections are intended to transform the equation \eqref{eq:1.1} \begin{equation}\label{eq:1.1} x(t) +…

We describe an algorithm, based on Euler's method, for solving Volterra integro-differential equations. The algorithm approximates the relevant integral by means of the composite Trapezium Rule, using the discrete nodes of the independent…

In the present note we give an explicit integration of some two--dimensionalised Lotka--Volterra type equations associated with simple Lie algebras, other than the familiar $A_n$ case, possessing a representation without branching. This…

The variational local moment approach (V-LMA), being a modification of the method due to Logan {\it et al}., is presented here. The existence of local moments is taken from the outset and their values are determined through variational…

In this paper, a computational method is developed to find an approximate solution of the stochastic Volterra-Fredholm integral equation using the Walsh function approximation and its operational matrix. Moreover, convergence and error…

This paper focuses on the optimal control of a class of stochastic Volterra integral equations. Here the coefficients are regular and not assumed to be of convolution type. We show that, under mild regularity assumptions, these equations…

In this paper we study the unique solvability of backward stochastic Volterra integral equations (BSVIEs in short), in terms of both the M-solutions introduced in [17] and the adapted solutions in [6], [12] or [14]. A general existence and…

The note is devoted to estimates for convolutions appearing in some class of stochastic Volterra equations. Two maximal inequalities and exponential tail estimate are proved by the fractional method of infinite dimensional stochastic…

In this paper, a two-dimensional operational matrix method based on Chelyshkov polynomials is implemented to numerically solve the two-dimensional stochastic It\^o-Volterra Fredholm integral equations. These equations arise in several…

This paper presents a direct numerical scheme to approximate the solution of all classes of nonlinear Volterra integral equations of the first kind. This computational method is based on operational matrices and vectors. The operational…

We study a class of nonlinear Volterra integral equations that generalize the classical capillary rise models, allowing for nonsmooth kernels and nonlinearities. To accommodate such generalities, we work in two families of function spaces:…

We prove strong existence and uniqueness, and H\"older regularity, of a large class of stochastic Volterra equations, with singular kernels and non-Lipschitz diffusion coefficient. Extending Yamada-Watanabe's theorem, our proof relies on an…

In this paper stochastic Volterra equations admitting exponentially bounded resolvents are studied. After obtaining convergence of resolvents, some properties for stochastic convolutions are studied. Our main result provide sufficient…

We introduce a numerical method for the solution of the time-dependent Schrodinger equation with a smooth potential, based on its reformulation as a Volterra integral equation. We present versions of the method both for periodic boundary…

The discrete autonomous/non-autonomous Toda equations and the discrete Lotka-Volterra system are important integrable discrete systems in fields such as mathematical physics, mathematical biology and statistical physics. They also have…

In this paper, we use a numerical method that involves hybrid and block-pulse functions to approximate solutions of systems of a class of Fredholm and Volterra integro-differential equations. The key point is to derive a new approximation…

Two different Sinc-collocation methods for Volterra integral equations of the second kind have been independently proposed by Stenger and Rashidinia--Zarebnia. However, their relation remains unexplored. This study theoretically examines…