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A polynomial collocation method for the numerical solution of weakly singular and singular integral equations on non‐smooth boundaries
Author(s) -
Monegato G.,
Scuderi L.
Publication year - 2003
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.843
Subject(s) - mathematics , smoothing , singular integral , singular solution , collocation (remote sensing) , chebyshev polynomials , singular point of a curve , collocation method , polynomial , mathematical analysis , numerical analysis , transformation (genetics) , regular singular point , variable (mathematics) , simple (philosophy) , matrix (chemical analysis) , integral equation , differential equation , computer science , ordinary differential equation , biochemistry , statistics , chemistry , philosophy , materials science , epistemology , machine learning , composite material , gene
The aim of this paper is to show the efficiency of the use of smoothing changes of variable in the numerical treatment of 1D and 2D weakly singular and singular integral equations. The introduction of a smoothing transformation, besides smoothing the solution, allows also the use of a very simple and efficient collocation method based on Chebyshev polynomials of the first kind and their zeros. Further, we propose proper smoothing changes of variable also for the numerical approximation of those collocation matrix elements, which are given by weakly singular, singular or nearly singular integrals. Several numerical tests are given to point out the efficiency of the numerical approach we propose. Copyright © 2003 John Wiley & Sons, Ltd.