Titlebook: Continuum Mechanics, Applied Mathematics and Scientific Computing:Godunov‘s Legacy; A Liber Amicorum to Gennadii V. Demidenko,Evgeniy Rome

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Development of the Matrix Spectrum Dichotomy Method,The work provides a systematic review of algorithms and applications of the dichotomy problem of the matrix spectrum. This problem is a promising alternative to the asymmetric spectral problem in the classical formulation.

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An All-Regime and Well-Balanced Lagrange-Projection Scheme for the Shallow Water Equations on UnstrWe are interested in the numerical approximation of the shallow water equations in two space dimensions. We propose a well-balanced, all-regime, and positive scheme. Our approach is based on a Lagrange-projection decomposition which allows to naturally decouple the acoustic and transport terms.

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On Estimates of Solutions to One Class of Functional Difference Equations with Periodic CoefficientIn the present paper, we consider a class of functional difference equations with periodic coefficients. We establish criteria for asymptotic stability of the zero solution to the equations and obtain estimates characterizing the decay rates of solutions to these equations at infinity.

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An Easy Control of the Artificial Numerical Viscosity to Get Discrete Entropy Inequalities When App general, very difficult to obtain. In the present work, we present a suitable control of the numerical artificial viscosity in order to recover the expected discrete entropy inequalities. Moreover, the artificial viscosity control turns out to be very easy and the resulting numerical implementation is very convenient.