Weighted Uniform Convergence of the Quadrature Method for Cauchy Singular Integral Equations

1996 ◽  
pp. 153-181 ◽  
Author(s):  
Maria Rosaria Capobianco ◽  
Peter Junghanns ◽  
Uwe Luther ◽  
Giuseppe Mastroianni
Keyword(s):  
Uniform Convergence ◽  
Integral Equations ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Quadrature Method ◽  
Cauchy Singular Integral

scholarly journals A quadrature method for constant-coefficient Cauchy singular integral equations on an interval

2000 ◽  
Vol 42 (2) ◽  
pp. 287-311
Author(s):  
Youngmok Jeon
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Constant Coefficient ◽  
Order Of Convergence ◽  
Singular Integral Equations ◽  
Variable Coefficients ◽  
Trapezoidal Rule ◽  
Stability And Convergence ◽  
Quadrature Method ◽  
Cauchy Singular Integral

AbstractWe consider a mesh grading quadrature method for real constant-coefficient Cauchy singular integral equations of index 0. The quadrature method is based on the trapezoidal rule. A complete stability and convergence analysis is given by the use of the noncompact perturbation analysis as in Jeon [10] and Elschner and Stephan [7]. The order of convergence can be arbitrarily high if the order of mesh grading is high enough. We also provide an efficient way of evaluating asymptotics of the solution at the end points. Experimentally, we observe that the method also works well for Cauchy singular integral equations with variable coefficients.

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