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A heat approximation

Miroslav Dont (2000)

Applications of Mathematics

The Fourier problem on planar domains with time variable boundary is considered using integral equations. A simple numerical method for the integral equation is described and the convergence of the method is proved. It is shown how to approximate the solution of the Fourier problem and how to estimate the error. A numerical example is given.

A -stable methods of high order for Volterra integral equations

Ľubor Malina (1975)

Aplikace matematiky

Method for numerical solution of Volterra integral equations, based on the O.I.M. methods, is suggested. It is known that the class of O.I.M. methods includes A -stable methods of arbitrary high order of asymptotic accuracy. In part 5, it is proved that these methods generate methods for numerical solution of Volterra equations which are also A -stable and of an arbitrarily high order. There is one advantage of the methods. Namely, they need no matrix inversion in the course of their numerical realization....

Approximate solutions for integrodifferential equations of the neutral type

B. G. Pachpatte (2010)

Commentationes Mathematicae Universitatis Carolinae

The main objective of the present paper is to study the approximate solutions for integrodifferential equations of the neutral type with given initial condition. A variant of a certain fundamental integral inequality with explicit estimate is used to establish the results. The discrete analogues of the main results are also given.

Approximation of abstract linear integrodifferential equations

Hirokazu Oka, Naoki Tanaka (2000)

Studia Mathematica

This paper is devoted to the approximation of abstract linear integrodifferential equations by finite difference equations. The result obtained here is applied to the problem of convergence of the backward Euler type discrete scheme.

Convergenza per l'equazione degli integrali primi associata al problema del rimbalzo

Michele Carriero, Antonio Leaci, Eduardo Pascali (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In this paper we present a few results on convergence for the prime integrals equations connected with the bounce problem. This approach allows both to prove uniqueness for the one-dimensional bounce problem for almost all permissible Cauchy data (see also [6]) and to deepen previous results (see [3], [5], [7]).

Defect correction and a posteriori error estimation of Petrov-Galerkin methods for nonlinear Volterra integro-differential equations

Shu Hua Zhang, Tao Lin, Yan Ping Lin, Ming Rao (2000)

Applications of Mathematics

We present two defect correction schemes to accelerate the Petrov-Galerkin finite element methods [19] for nonlinear Volterra integro-differential equations. Using asymptotic expansions of the errors, we show that the defect correction schemes can yield higher order approximations to either the exact solution or its derivative. One of these schemes even does not impose any extra regularity requirement on the exact solution. As by-products, all of these higher order numerical methods can also be...

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