Economical unconditionally stable locally-implicit finite difference schemes for 2-D hyperbolic systems

A new approach for the construction of economical algorithms (of the first and second order of accuracy) for the solution of linear hyperbolic systems is presented. Its main elements are independent calculation of fluxes in each spatial direction and locally – implicit difference scheme for the solution of one-dimensional hyperbolic systems in which the implicit scheme is used if and only if the corresponding Courant number is greater than one.