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The monotonic bicompact schemes for a linear transfer equation

B. V. Rogov^a, M. N. Mikhailovskaya<sup>b

a</sup> Keldysh Institute of Applied Mathematics of RAS, Moscow
^b Moscow Institute of Physics and Technology, State University

Abstract: It is shown that previously proposed by the authors bicompact difference scheme for a linear transport equation, which has the fourth-order approximation in spatial coordinate on a two-point stencil and the first order approximation in time, is monotonic. This implicit scheme is absolutely stable and can be solved by explicit formulas of the running calculation method. On the basis of this scheme the monotone nonlinear homogeneous difference scheme of high (third for smooth solutions) order accuracy in time is constructed. Calculations of the test problems with discontinuous solutions showed a significant advantage in the accuracy of the proposed scheme over known nonoscillatory schemes of high-order approximation.

Keywords: transport equation, bicompact difference schemes, monotonicity.

UDC: 519.6

Received: 14.12.2010

 English version: Mathematical Models and Computer Simulations, 2012, 4:1, 92–100

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