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A pointwise estimate for the solution to a linear Volterra integral equation

Angelo Morro (1983)

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

Utilizzando una generalizzazione della disuguaglianza di Gronwall si fornisce una stima puntuale per la soluzione dell’equazione lineare integrale di Volterra di seconda specie. Tale stima può essere applicata utilmente anche nello studio della stabilità di equazioni di evoluzione per mezzi continui.

A singular initial value problem for the equation u ( n ) ( x ) = g ( u ( x ) )

Wojciech Mydlarczyk (1998)

Annales Polonici Mathematici

We consider the problem of the existence of positive solutions u to the problem u ( n ) ( x ) = g ( u ( x ) ) , u ( 0 ) = u ' ( 0 ) = . . . = u ( n - 1 ) ( 0 ) = 0 (g ≥ 0,x > 0, n ≥ 2). It is known that if g is nondecreasing then the Osgood condition δ 1 / s [ s / g ( s ) ] 1 / n d s < is necessary and sufficient for the existence of nontrivial solutions to the above problem. We give a similar condition for other classes of functions g.

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....

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