The optimization of methods of solving boundary value problems with a boundary layer

摘要: Abstract THE solutions of a number value problems for differential equations with small parameters having higher derivatives possess singularities the boundary layer type [1, 2]. For solution such by finite-difference methods integration step near must be substantially less than thickness which is characteristic dimension problem. In case constant steps throughout whole region this circumstance leads to considerable increase in volume calculations when are reduced derivatives. An exception may only so-called “quasiclassical approximations” [3], adapted specially derivatives, but these can written isolated classes ordinary equations. The use asymptotic [2, 4] requires rather small, and their coefficients very smooth. same often applies numerical methods. Below we construct, two model (a set an elliptic equation), on network variable evaluation error homogeneous parameter, few constraints smoothness coefficients.