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On the approximate solution of some two‐dimensional singular integral equations
Author(s) -
Didenko V. D.,
Silbermann B.
Publication year - 2001
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.265
Subject(s) - mathematics , orthonormality , quadrature (astronomy) , integral equation , fourier integral operator , singular integral , basis (linear algebra) , class (philosophy) , mathematical analysis , partial differential equation , differential equation , orthonormal basis , computer science , physics , geometry , quantum mechanics , artificial intelligence , electrical engineering , engineering
Abstract An approximation method for a wide class of two‐dimensional integral equations is proposed. The method is based on using a special function system. Orthonormality and good interaction with fundamental integral operators arising in partial differential equations are remarkable properties of this system. In addition, all the basis elements can easily be calculated by recurrence relations. Taking into account these properties we construct a numerical algorithm which does not require additional effort (such as quadrature) to compute the values of the fundamental operators on the basis elements. Copyright © 2001 John Wiley & Sons, Ltd.