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Approximate properties of principal solutions of Volterra-type integrodifferential equations with infinite aftereffect

Yu. A. Ryabov (1995)

Mathematica Bohemica

The integrodifferential system with aftereffect (“heredity” or “prehistory”) dx/dt=Ax+-t R(t,s)x(s,)ds, is considered; here ε is a positive small parameter, A is a constant n × n matrix, R ( t , s ) is the kernel of this system exponentially decreasing in norm as t . It is proved, if matrix A and kernel R ( t , s ) satisfy some restrictions and ε does not exceed some bound ε * , then the n -dimensional set of the so-called principal two-sided solutions x ˜ ( t , ε ) approximates in asymptotic sense the infinite-dimensional set of solutions...

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 by nonlinear integral operators in some modular function spaces

Carlo Bardaro, Julian Musielak, Gianluca Vinti (1996)

Annales Polonici Mathematici

Let G be a locally compact Hausdorff group with Haar measure, and let L⁰(G) be the space of extended real-valued measurable functions on G, finite a.e. Let ϱ and η be modulars on L⁰(G). The error of approximation ϱ(a(Tf - f)) of a function f ( L ( G ) ) ϱ + η D o m T is estimated, where ( T f ) ( s ) = G K ( t - s , f ( t ) ) d t and K satisfies a generalized Lipschitz condition with respect to the second variable.

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.

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