Local Theory of a Collocation Method for Cauchy Singular Integral Equations on an Interval

نویسندگان

  • Peter Junghanns
  • Uwe Weber
چکیده

We consider a collocation method for Cauchy singular integral equations on the interval based on weighted Chebyshev polynomials, where the coe cients of the operator are piecewise continuous. Stability conditions are derived using Banach algebra methods, and numerical results are given.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

An effective method for approximating the solution of singular integral equations with Cauchy kernel type

In present paper, a numerical approach for solving Cauchy type singular integral equations is discussed. Lagrange interpolation with Gauss Legendre quadrature nodes and Taylor series expansion are utilized to reduce the computation of integral equations into some algebraic equations. Finally, five examples with exact solution are given to show efficiency and applicability of the method. Also, w...

متن کامل

A Nodal Spline Collocation Method for the Solution of Cauchy Singular Integral Equations

In this paper we introduce a nodal spline collocation method for the numerical solution of Cauchy singular integral equations. Uniform error bounds of the approximate solution are provided and some numerical examples are presented. c © 2008 European Society of Computational Methods in Sciences and Engineering

متن کامل

A collocation scheme for a certain Cauchy singular integral equation based on the superconvergence analysis

In this paper, we investigate the composite midpoint rule for the evaluation of Cauchy principal value integral in an interval and place the key point on its pointwise superconver-gence phenomenon. The error expansion of the rule is obtained, which shows that the superconvergence phenomenon occurs at the points of each subinterval whose local coordinate is the zeros of some function. Then, by a...

متن کامل

Approximate solution of dual integral equations

‎We study dual integral equations which appear in formulation of the‎ ‎potential distribution of an electrified plate with mixed boundary‎ ‎conditions‎. ‎These equations will be converted to a system of‎ ‎singular integral equations with Cauchy type kernels‎. ‎Using‎ ‎Chebyshev polynomials‎, ‎we propose a method to approximate the‎ ‎solution of Cauchy type singular integral equation which will ...

متن کامل

Application of Chebyshev Polynomials for Solving Abel's Integral Equations of the First and Second Kind

In this paper, a numerical implementation of an expansion method is developed for solving Abel's integral equations of the first and second kind. The solution of such equations may demonstrate a singular behaviour in the neighbourhood of the initial point of the interval ofintegration. The suggested method is based on the use of Taylor series expansion to overcome the singularity which le...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1997