On a boundary value problem for the equations of a viscous heat-conducting gas in noncylindrical domains shrinking in time

Kaliev, I. A.; Podkuiko, M. S.

doi:10.1134/s0012266106100077

Cited by 10 publications

(1 citation statement)

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“…We have given a direct proof that the linear inequality (2.11) follows from the nonlinear inequality (2.12) for u(T ) . We could also come to this result if we used the Bihari lemma [17,18] or a more particular result -the Vaigant inequality [19,20].…”

Section: Problem Formulationmentioning

confidence: 99%

Numerical solution of the Cauchy problem for Volterra integrodifferential equations with difference kernels

Vabishchevich¹

2021

Preprint

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We consider the problems of the numerical solution of the Cauchy problem for an evolutionary equation with memory when the kernel of the integral term is a difference one. The computational implementation is associated with the need to work with an approximate solution for all previous points in time. In this paper, the considered nonlocal problem is transformed into a local one; a loosely coupled equation system with additional ordinary differential equations is solved. This approach is based on the approximation of the difference kernel by the sum of exponentials. Estimates for the stability of the solution concerning the initial data and the right-hand side for the corresponding Cauchy problem are obtained. Two-level schemes with weights with convenient computational implementation are constructed and investigated. The theoretical consideration is supplemented by the results of the numerical solution of the integrodifferential equation when the kernel is the stretching exponential function.

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