In this lecture we introduce and discuss some numerical methods, based on new results of polynomial approximation, for solving Fredholm integral equations of the second kind in the spaces of continuous functions equipped with certain uniform weighted norms, where is the unknown function, and are given functions, is a weight function, and is a finite interval or the real semiaxis . Also, we mention some results for the Cauchy singular integral equations. The case we treat with the Jacobi weight and the case on half-line with the generalized Laguerre weight Assuming the continuity of the kernel we use Nyström methods and prove the stability, the convergence and the well-conditioning of the corresponding matrices. Error estimates and numerical tests are also included.
Примечание. Тезисы докладов публикуются в авторской редакции
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© 1996-2000, Институт вычислительных технологий СО РАН, Новосибирск
© 1996-2000, Сибирское отделение Российской академии наук, Новосибирск