Geodesic
Bases derived from trigonometry and their advantages
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 13 (2013) no. 1, pp. 105-119 Cet article a éte moissonné depuis la source Math-Net.Ru

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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
Mots-clés : conjugate conditions. 
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V. V. Smelov. Bases derived from trigonometry and their advantages. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 13 (2013) no. 1, pp. 105-119. http://geodesic.mathdoc.fr/item/VNGU_2013_13_1_a9/

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