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

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.


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