The K-th order of accuracy semiexplicit K-step scheme for transport equation is derived. The theoretical analysis of positivity, monotonicity and stability of the weighted semiexplicit two and three step schemes is presented. This analysis shows that both schemes are unconditionally stable and have improved in comparison with the diamond difference scheme monotonicity properties. A few numerical examples, that confirm these conclusions are presented. We also give a generalization of the semiexplicit K-step scheme for nodal schemes. An example of physical problem of charged particles transport in external electric field, for which the using of semiexplicit K-step scheme seems useful and quite effective is discussed.
Publication language:russian, pages:31
Research direction:
Mathematical problems and theory of numerical methods
