Difference schemes for drain transfer equation based on space of undefined coefficients analysis

A family of finite difference schemes for linear transfer equation numerical solution on an explicit five-point stencil is considered. A generalized approximation condition has been used to investigate differential schemes. Analysis of the difference schemes in the space of undefined coefficients is carried out. The problem of an optimal difference scheme constructing is reduced to the problem of linear programming. A family of hybrid difference schemes is also considered. For them, the hybrid parameter will be a locally computed dimensionless wave number. The analysis also shows that when schemes of increased approximation order are constructed, their local properties will be determined by a halved (compared to the first approximation order scheme) dimensionless wavenumber.
A family of difference schemes for a linear drain transfer equation solving is also built. To solve the linear drain transfer equation more solutions to the linear programming problem are available among the optimal schemes of increased approximation order on a non-expanded stencil (compact schemes). The properties of optimal schemes of increased approximation order in the case of a drain equation are determined by a dimensionless parameter depending on both the wavenumber and the drain factor. The difference schemes for the drain transfer equation have slightly better than for homogeneous linear equation. It is advisable to allocate a part with linear drain and to build a hybrid difference schemes for hyperbolic-type systems solution by the splitting method.
Numerical examples of implemented schemes for the simple linear equations are given.