High accuracy finite-difference method for boundary layer equations

The numerical method of high order approximation is suggested for solution of nonlinear equations system of parabolic type with boundary condition of general type. By means of introduction of new unknown functions the initial differential equations system is reduced to the system of first-order equations. Then this partial differential equations system is reduced to the system of ordinary differential equations with respect to crosslayer coordinate $\zeta$ it is linearized, in suitable way andis solved on the basis of implicit difference six-order scheme relatively $\Delta\zeta$. The solution of this system of algebraic linear equations is based upon the variant of three-diagonal solver method, which enables one to realize calculations in standard way for general type of the boundary conditions.