𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Stability and Convergence of a Hyperbolic Tangent Method for Singular Integral Equations

✍ Scribed by Ezio Venturino

Publisher
John Wiley and Sons
Year
1993
Tongue
English
Weight
899 KB
Volume
164
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

In this paper we reexamine a previously proposed quadrature scheme, [VENTURINO], based on a formula proposed in [STENGER, 1976]. Our goal is to establish a stability result for the dominant singular integral equation of index one, and from it derive the error analysis for the proposed numerical method. The convergence of the method can then be extended to the first kind complete equation and to the equation of index zero. Finally the modifications necessary for applying this analysis to a recently proposed scheme for Hadamard finite part integral equations are examined. In all these proofs the necessary assumption we need to make is to restrict our considerations to a compact subset of the interval in which the equation is formulated, containing all the nodes where the unknown is evaluated.

πŸ“œ SIMILAR VOLUMES

The Stability and the Convergence of a C
The Stability and the Convergence of a Collocation Method for a Class of Cauchy Singular Integral Equations
✍ Maria Rosaria Capobianco πŸ“‚ Article πŸ“… 1993 πŸ› John Wiley and Sons 🌐 English βš– 520 KB

## Abstract The author proves the stability and the uniform convergence of a collocation method for solving Cauchy singular integral equations with regular pertubation kernel. Error estimates in the uniform norm are also given.