Related papers: Numerical Solution of Multiple Nonlinear Volterra …
In this work, we consider a boundary value problem for nonlinear triharmonic equation. Due to the reduction of nonlinear boundary value problems to operator equation for nonlinear terms we establish the existence, uniqueness and positivity…
In this work we prove that a family of explicit numerical finite-difference methods is convergent when applied to a nonlinear Volterra equation with a power-type nonlinearity. In that case the kernel is not of Lipschitz type, therefore the…
The first step when solving an infinite-dimensional eigenvalue problem is often to discretize it. We show that one must be extremely careful when discretizing nonlinear eigenvalue problems. Using examples, we show that discretization can:…
We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.
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 this paper, we present a collocation method for nonlinear Volterra integral equation of the first kind. This method benefits from the idea of $hp$-version projection methods. We provide an approximation based on the Legendre polynomial…
In this work, we introduce a novel numerical method for solving initial value problems associated with a given differential. Our approach utilizes a spline approximation of the theoretical solution alongside the integral formulation of the…
We demonstrate the construction of an explicit NSFD discretization for the standard Lotka-Volterra equations. In contrast to previous NSFD schemes, our representation is dynamic consistent with respect to all the essential properties of the…
In the present paper, a Nystrom-type method for second kind Volterra integral equations is introduced and studied. The method makes use of generalized Bernstein polynomials, defined for continuous functions and based on equally spaced…
We offer a simple method Monte Carlo for computation of Volterra's and spherical type multiple integrals with weak (integrable) singularities. An elimination of infinity of variance is achieved by incorporating singularities in the density,…
A M\"untz spectral collocation method is implemented for solving weakly singular Volterra integro-differential equations (VDIEs) with proportional delays. After constructing the numerical scheme to seek an approximate solution, we derive…
Our study aims to specify the asymptotic error distribution in the discretization of a stochastic Volterra equation with a fractional kernel. It is well-known that for a standard stochastic differential equation, the discretization error,…
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…
The linearization of nonlinear systems is an important digital enhancement technique. In this paper, a real-time capable post- and pre-linearization method for the widely applicable time-varying discrete-time Volterra series is presented.…
A class of nonlocal nonlinear wave equation arises from the modeling of a one dimensional motion in a nonlinearly, nonlocally elastic medium. The equation involves a kernel function with nonnegative Fourier transform. We discretize the…
Two discretizations of the vector nonlinear Schrodinger (NLS) equation are studied. One of these discretizations, referred to as the symmetric system, is a natural vector extension of the scalar integrable discrete NLS equation. The other…
The present study proposed a method for numerical solution of linear Volterra integral equations (VIEs) of the third kind, before only analytical solution methods had been discussed with reference to previous research and review of the…
This article presents a novel solution method for nonautonomous linear ordinary fractional differential equations. The approach is based on reformulating the analytical solution using the $\star$-product, a generalization of the Volterra…
The paper focuses on solving one class of Volterra equations of the first kind, which is characterized by the variability of all integration limits. These equations were introduced in connection with the problem of identifying nonsymmetric…
This paper is devoted to overview of the authors works for numerical solution of singular integral equations (SIE), polysingular integral equations and multi-dimensional singular integral equations of the second kind. The authors…