Related papers: A reduction algorithm for Volterra integral equati…
The algebraic study of special integral operators led to the notions of Rota-Baxter operators and shuffle products which have found broad applications. This paper carries out an algebraic study of general integral operators and equations,…
Volterra's integral equations with local and nonlocal loads represent the novel class of integral equations that have attracted considerable attention in recent years. These equations are a generalisation of the classic Volterra integral…
We formulate and analyze a hybrid system model that involves Volterra integral operators with multiple integrals and two types of impulsive terms. We give a constructive proof, via an iteration method, of existence and uniqueness of…
We analyze a discretization method for solving nonlinear integral equations that contain multiple integrals. These equations include integral equations with a Volterra series, instead of a single integral term, on one side of the equation.…
A concise overview of the spectral theory of integral-functional operators is provided. In the context of analysis, a technique is described for deriving solutions to equations involving operators in a closed form. A constructive theorem…
We study classical solutions (existence, uniqueness, and explicit solution operator) for homogeneous, linear, and semilinear abstract Volterra integral equations of wave type with almost sectorial operators. We use a functional calculus for…
Weakly singular Volterra integral equations of the different types are considered. The construction of accuracy-optimal numerical methods for one-dimensional and multidimensional equations is discussed. Since this question is closely…
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…
The systems of nonlinear Volterra integral equations of the first kind with jump discontinuous kernels are studied. The iterative numerical method for such nonlinear systems is proposed. Proposed method employs the modified…
A vector partition function is the number of ways to write a vector as a non-negative integer-coefficient sum of the elements of a finite set of vectors $\Delta$. We present a new algorithm for computing closed-form formulas for vector…
Some results about existence, uniqueness, and attractive behaviour of solutions for nonlinear Volterra integral equations with non-convolution kernels are presented in this paper. These results are based on similar ones about nonlinear…
The variational iteration method is used to solve nonlinear Volterra integral equations. Two approaches are presented distinguished by the method to compute the Lagrange multiplier.
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.
The spinless Salpeter equation presents a rather particular differential operator. In this paper we rewrite this equation into integral and integro-differential equations. This kind of equations are well known and can be more easily…
We study some mapping properties of Volterra type integral operators and composition operators on model spaces. We also discuss and give out a couple of interesting open problems in model spaces where any possible solution of the problems…
A new expression for solving homogeneous linear ODEs based on a generalization of the Volterra composition was recently introduced. In this work, we extend such an expression, showing that it corresponds to inverting an infinite matrix.…
We propose the numerical methods for solution of the weakly regular linear and nonlinear evolutionary (Volterra) integral equation of the first kind. The kernels of such equations have jump discontinuities along the continuous curves…
We study a numerical approximation for a nonlinear variable-order fractional differential equation via an integral equation method. Due to the lack of the monotonicity of the discretization coefficients of the variable-order fractional…
The reduction of a large number of scalar integrals to a small set of master integrals via Laporta's algorithm is common practice in multi-loop calculations. It is also a major bottleneck in terms of running time and memory consumption. It…
We obtain asymptotic results for well known summatory arithmetic functions, such as $\psi(x),$ and establish connections to new summatory functions. A new Volterra integral equation is offered, which is solved by summatory arithmetic…