Keeping of the high approximation order during the solution of stiff partial-differential equations systems at a given accuracy of little terms

High order (higher, then second) of numerical solution approximation of stiff equations systems with little terms – the Navier–Stokes, Reynolds equations and the wave equation – is important on principle. The necessity of solutions of that systems will stimulated the growth of the methods accuracy into computational mathematics. The factors are discussed (capturing of discontinuity of functions and their derivatives, differential forms of conservation lows, local representation of multiplication terms, monotonization), which had reduced the approximation order of the solution up to the second or first under the unsuccessful construction of the method. For the capturing of this factors it is need the new philosophy of method constructions, progress of high accuracy algorithms. Some recommendations are given.