Open AccessNUMERICAL SOLUTIONS AND THEIR SUPERCONVERGENCE FOR WEAKLY SINGULAR INTEGRAL EQUATIONS WITH DISCONTINUOUS COEFFICIENTS
Author(s) -
Kristiina Hakk,
Arvet Pedas
Publication year - 1998
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 - 10.3846/13926292.1998.9637093
Subject(s) - superconvergence , mathematics , piecewise , collocation (remote sensing) , collocation method , convergence (economics) , polynomial , mathematical analysis , orthogonal collocation , interval (graph theory) , integral equation , ordinary differential equation , finite element method , differential equation , combinatorics , computer science , machine learning , economic growth , economics , thermodynamics , physics
The piecewise polynomial collocation method is discussed to solve second kind Fredholm integral equations with weakly singular kernels K (t, s) which may be discontinuous at s = d, d = const. The main result is given in Theorem 4.1. Using special collocation points, error estimates at the collocation points are derived showing a more rapid convergence than the global uniform convergence in the interval of integration available by piecewise polynomials.