Approximate Solution of Some Linear Nonhomogeneous Operator Equations by Approach Alternative to Asymptotic Method

摘要

Problems of approximate solution of some linear nonhomogeneous operator equation with an approach alternative to asymptotic method is studied. The alternative method is based on representation of unknown vector over the small parameter with orthogonal series instead of asymptotic one. In such a case system of three-point operator equations of special structure in received. For system solving a certain regular method is used. On the basis of the suggested method the programming production is created and realized by means of computer. Algorithms and program products represent a new technology of approximate solving of two-point boundary value problem, some linear nonhomogeneous integro - differential equations and singular integral equations containing an immovable singularity.