
Twolevel schemes for the advection equation
The advection equation is the basis for mathematical models of continuum...
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Splitting methods for solution decomposition in nonstationary problems
In approximating solutions of nonstationary problems, various approaches...
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Twocomponent domain decomposition scheme with overlapping subdomains for parabolic equations
An iterationfree method of domain decomposition is considered for appro...
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General Midpoint Subdivision
In this paper, we introduce two generalizations of midpoint subdivision ...
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Markov Neural Operators for Learning Chaotic Systems
Chaotic systems are notoriously challenging to predict because of their ...
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On the stability of timediscrete dynamic multiple network poroelasticity systems arising from secondorder implicit timestepping schemes
The classical Biot's theory provides the foundation of a fully dynamic p...
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Second Order Operators in the NASA Astrophysics Data System
Second Order Operators (SOOs) are database functions which form secondar...
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Splitting Schemes for Some SecondOrder Evolution Equations
We consider the Cauchy problem for a secondorder evolution equation, in which the problem operator is the sum of two selfadjoint operators. The main feature of the problem is that one of the operators is represented in the form of the product of operator A by its conjugate A*. Time approximations are carried out so that the transition to a new level in time was associated with a separate solution of problems for operators A and A*, not their products. The construction of unconditionally stable schemes is based on general results of the theory of stability (correctness) of operatordifference schemes in Hilbert spaces and is associated with the multiplicative perturbation of the problem operators, which lead to stable implicit schemes. As an example, the problem of the dynamics of a thin plate on an elastic foundation is considered.
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