Collocation and quadrature methods for solving singular integral equations with piecewise continuous coefficients. (English) Zbl 1124.65121

Capcelea, Titu

Bul. Acad. Ştiinţe Repub. Mold., Mat. 2006, No. 3(52), 27-44 (2006).

The author investigates computation schemes of collocation and mechanical quadrature methods for an approximate solving of complete singular integral equations with piecewise continuous coefficients, a weakly singular and regular kernel using the Arzela-Ascoli theorem and the Banach theorem in operator theory based on the theory of classical singular integral equations of analytic functions with one complex variable.

Reviewer: Hu Chuangan (Tianjin)

MSC:

65R20	Numerical methods for integral equations
45E05	Integral equations with kernels of Cauchy type
45F15	Systems of singular linear integral equations
45G05	Singular nonlinear integral equations

Keywords:

Cauchy singular integral equation; piecewise continuous coefficient; collocation method; quadrature method; Arzela-Ascoli theorem; Banach theorem