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On a contact problem for a viscoelastic von Kármán plate and its semidiscretization

Igor Bock, Ján Lovíšek (2005)

Applications of Mathematics

We deal with the system describing moderately large deflections of thin viscoelastic plates with an inner obstacle. In the case of a long memory the system consists of an integro-differential 4th order variational inequality for the deflection and an equation with a biharmonic left-hand side and an integro-differential right-hand side for the Airy stress function. The existence of a solution in a special case of the Dirichlet-Prony series is verified by transforming the problem into a sequence of...

On a reliable solution of a Volterra integral equation in a Hilbert space

Igor Bock, Ján Lovíšek (2003)

Applications of Mathematics

We consider a class of Volterra-type integral equations in a Hilbert space. The operators of the equation considered appear as time-dependent functions with values in the space of linear continuous operators mapping the Hilbert space into its dual. We are looking for maximal values of cost functionals with respect to the admissible set of operators. The existence of a solution in the continuous and the discretized form is verified. The convergence analysis is performed. The results are applied to...

On convergence of quadrature-differences method for linear singular integro-differential equations on the interval

A. I. Fedotov (2001)

Archivum Mathematicum

Here we propose and justify the quadrature-differences method for the full linear singular integro-differential equations with Cauchy kernel on the interval ( - 1 , 1 ) . We consider equations of zero, positive and negative indices. It is shown, that the method converges to exact solution and the error estimate depends on the sharpness of derivative approximation and the smoothness of the coefficients and the right-hand side of the equation.

On numerical solution to the problem of reactor kinetics with delayed neutrons by Monte Carlo method

Jan Kyncl (1994)

Applications of Mathematics

In this paper, the linear problem of reactor kinetics with delayed neutrons is studied whose formulation is based on the integral transport equation. Besides the proof of existence and uniqueness of the solution, a special random process and random variables for numerical elaboration of the problem by Monte Carlo method are presented. It is proved that these variables give an unbiased estimate of the solution and that their expectations and variances are finite.

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