Higher-Order Difference Schemes in Heat- and Mass-Transfer Problems

Studies of many physical processes lead to the numerical solution of boundary-value problems for macroequations with a small parameter. Classical difference schemes poorly describe the solution of the original differential problem in boundary-layer regions, because they have an approximation viscosity comparable with the mesh size. This paper proposes difference schemes of higher order of approximation, which allow one to adequately simulate the motion of a viscous fluid in a wide range of Reynolds numbers, as well as reduce the time and amount of calculations due to the efficiency of the methods used in numerical simulation.