Open AccessPRODUCT QUASI-INTERPOLATION IN LOGARITHMICALLY SINGULAR INTEGRAL EQUATIONS
Author(s) -
Eero Vainikko,
Gennadi Vainikko
Publication year - 2012
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.2012.736089
Subject(s) - mathematics , interpolation (computer graphics) , kernel (algebra) , mathematical analysis , fredholm integral equation , variable (mathematics) , product (mathematics) , interval (graph theory) , boundary (topology) , integration by parts , diagonal , logarithm , class (philosophy) , integral equation , pure mathematics , geometry , computer science , animation , computer graphics (images) , combinatorics , artificial intelligence
A discrete high order method is constructed and justified for a class of Fredholm integral equations of the second kind with kernels that may have boundary and logarithmic diagonal singularities. The method is based on the improving the boundary behaviour of the kernel with the help of a change of variables, and on the product integration using quasi-interpolation by smooth splines of order m. Properties of different proposed calculation schemes are compared through numerical experiments using, in particular, variable precision interval arithmetics.