A CLASS OF NUMERICAL ALGORITHMS, CONSERVATIVE AT STABILIZATION, FOR MODELING TRANSPORT PROCESSES


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Abstract

We consider a class of effective two-step symmetrized algorithms for numerical modeling of processes defined by boundary-value problems for transport equations with boundary conditions of the third kind in cases of various approximations of the convection terms of the equation and different ways of writing the difference schemes with respect to time. We prove that the algorithms are unconditionally stable and show that they are economical. We find an approximation for physical conservation laws on grid sets and prove that the difference algorithms are conservative when the process stabilizes.

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