The bicompact monotonic schemes for a multidimensional linear transport equation

Bicompact difference schemes, previously proposed by the authors for the linear one-dimensional transport equations are generalized to the multidimensional case by using a coordinate-wise splitting of the multidimensional problem. The scheme stencil for each of the spatial directions is minimal and consists of two points. The schemes are efficient and can be solved by explicit formulas of the running calculation method. The proposed difference schemes have the fourth-order approximation in space variables and first or third-order approximation in time for smooth solutions. The schemes for solving multidimensional problems inherit the monotonicity property of one-dimensional bicompact schemes. Numerical examples that show the actual accuracy order of compact schemes for smooth solutions and the scheme monotonicity for jump-like solutions are given.