Computation of equations up to a prescribed accuracy with respect to singular terms and defect of differential equations. (English. Russian original) Zbl 1030.76041

Minailos, A. N.

Comput. Math. Math. Phys. 41, No. 10, 1489-1505 (2001); translation from Zh. Vychisl. Mat. Mat. Fiz. 41, No. 10, 1566-1582 (2001).

Boundary value problems for systems of differential equations with small coefficients of the highest order derivatives are considered in the following form \(U_t+F_x-\epsilon G_{xx}=0\), \(\varepsilon\ll{1}\). In the conventional approach, a solution is based on the construction of a grid that condenses in the regions where the terms containing \(\epsilon\) are essential. The author obtains estimates for the smallest admissible value of a parameter corresponding to the required accuracy of singular term, for the order of accuracy, and for the number of grid points.

Reviewer: Alexey Tret’yakov (Siedlce)

MSC:

76M20	Finite difference methods applied to problems in fluid mechanics
76N15	Gas dynamics (general theory)

Keywords:

singular term; small parameter; Navier-Stokes equations; order of accuracy; finite difference scheme; Reynolds averaged equations; wave equation; electromagnetic media