Results 1 to 10 of about 27,823 (314)

On the Stability of Numerical Methods for Nonlinear Volterra Integral Equations [PDF]

Discrete Dynamics in Nature and Society, 2010
Here we investigate the behavior of the analytical and numerical solution of a nonlinear second kind Volterra integral equation where the linear part of the kernel has a constant sign and we provide conditions for the boundedness or decay of solutions ...
E. Messina, Y. Muroya, E. Russo, A. Vecchio   +3 more
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A Unified Formulation of Analytical and Numerical Methods for Solving Linear Fredholm Integral Equations

Algorithms, 2021
This article is concerned with the construction of approximate analytic solutions to linear Fredholm integral equations of the second kind with general continuous kernels. A unified treatment of some classes of analytical and numerical classical methods,
Efthimios Providas
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Methods and effective algorithms for solving multidimensional integral equations

Российский технологический журнал, 2022
Objectives. Integral equations have long been used in mathematical physics to demonstrate existence and uniqueness theorems for solving boundary value problems for differential equations. However, despite integral equations have a number of advantages in
A. B. Samokhin
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A method for the numerical integration of ordinary differential equations [PDF]

Mathematics of Computation, 1958
where y(x) denotes the solution of the differential equation. The idea is to use a quadrature formula to estimate the integral of (1). This requires knowledge of the integrand at specified arguments xi in (x0, xo + h)-hence we require the values of y(x) at these arguments.
Stoller, L., Morrison, D.
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Numerical integration methods of the Vlasov equation [PDF]

Journal of Computational Physics, 1971
Abstract The methods of integrating the nonlinear Vlasov equation are reviewed, compared and interrelations are investigated. Another method is given which allows a truncation of the resulting infinite matrix without causing numerical instabilities. Its application to the linear and nonlinear Vlasov equation is discussed.
Glenn Joyce, Georg Knorr, Homer K Meier
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A numerical method for multidimensional Volterra integral equations

Applied Mathematical Sciences, 2022
In this paper, we introduce a new numerical procedure to solve multi-dimensional Volterra integral equations, based on the weighted mean-value theorem. Our method allows to determine a system of nonlinear equations, where the rst one is obtained via the application of the theoretical results, and the remaining ones are built through a Picard-like ...
Immacolata Oliva, Antonio Luciano Martire   +1 more
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On the Numerical Integration of Ordinary Differential Equations by Processed Methods [PDF]

SIAM Journal on Numerical Analysis, 2004
A one-step integrator \(\psi_h: \mathbb{R}^D\to \mathbb{R}^D\) with time step \(h\) for an ordinal differential equation \(x'= f(x)\), \(f: \mathbb{R}^D\to \mathbb{R}^D\), can be enhanced by ``processing'' based on a postprocessors \(\pi_h: \mathbb{R}^D\to \mathbb{R}^D\), to obtain a new integrator \(\widehat\psi_h:=\pi_h\circ\psi_h\circ \pi^{-1}_h ...
Sergio Blanes, Fernando Casas, Ander Murua   +2 more
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The Cardinal Spline Methods for the Numerical Solution of Nonlinear Integral Equations

Journal of Chemistry, 2020
In this study, an effective technique is presented for solving nonlinear Volterra integral equations. The method is based on application of cardinal spline functions on small compact supports.
Xiaoyan Liu, Jin Xie, Zhi Liu, Jiahuan Huang   +3 more
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An Effective Local Radial Basis Function Method for Solving the Delay Volterra Integral Equation of Nonvanishing and Vanishing Types

Journal of Mathematics, 2022
This paper presents a numerical method for solving a class of the delay Volterra integral equation of nonvanishing and vanishing types by applying the local radial basis function method.
Neda Khaksari, Mahmoud Paripour, Nasrin Karamikabir   +2 more
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A New Method of Numerical Integration of Differential Equations [PDF]

Mathematics of Computation, 1964
L'A. propose une méthode d'intégration approchée de \(y'=f(x, y)\) dans laquelle \(y'\) est évalué par extrapolation au début du pas et par substitution au milieu. Un exemple est donné. La méthode utilise, comme l'avait suggéré l'A. de cette analyse, à la fois le principe de Runge-Kutta et celui des méthodes à pas liés.
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