This article is cited in 1 paper

Bases derived from trigonometry and their advantages

V. V. Smelov

Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

Abstract: A specific use of trigonometric functions with respect to any interval possesses a high approximate quality. In this case, a solution of integral equations with kernels of the form $K(x-t)$ by the Galerkin method allows one to reduce the double integral to a very simple single integration. Also, a specific base of functions for solving problems with an elliptic operator with disconnected coefficients is proposed. A distinctive feature of this base is automatic realization of conjugate conditions in locations of discontinuities of coefficients of equations. Another essential property is a high-precise approximation of piecewise-smooth solutions of the above problems by means of a small number of base functions. All the proofs of the results obtained follow from the two theorems presented.

Keywords: problems with elliptic operator, discontinuous coefficients, piecewise-smooth basis functions, rapidly convergent series, approximation, minimization of square functional, integral equations, conjugate conditions.

UDC: 518.12+519.34

Received: 27.02.2012