The monotonic bicompact schemes for a linear transfer equation

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.