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Application of Richardson extrapolation with the Crank-Nicolson scheme for multi-dimensional advection

Zlatev, Zahari;  Dimov, Ivan;  Faragó, István;  Georgiev, Krassimir;  Havasi, Ágnes;  Ostromsky, Tzvetan — 2013

Applications of Mathematics 2013

Multi-dimensional advection terms are an important part of many large-scale mathematical models which arise in different fields of science and engineering. After applying some kind of splitting, these terms can be handled separately from the remaining part of the mathematical model under consideration. It is important to treat the multi-dimensional advection in a sufficiently accurate manner. It is shown in this paper that high order of accuracy can be achieved when the well-known Crank-Nicolson...

Applying approximate LU-factorizations as preconditioners in eight iterative methods for solving systems of linear algebraic equations

Zahari Zlatev;  Krassimir Georgiev — 2013

Open Mathematics

Many problems arising in different fields of science and engineering can be reduced, by applying some appropriate discretization, either to a system of linear algebraic equations or to a sequence of such systems. The solution of a system of linear algebraic equations is very often the most time-consuming part of the computational process during the treatment of the original problem, because these systems can be very large (containing up to many millions of equations). It is, therefore, important...

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