On the uniform convergence of Gaussian quadrature rules for Cauchy principal value integrals and their derivatives

The convergence of the aforementioned quadrature rules for integrands possessing H6lder-continuous derivatives of an appropriate order is proved to be uniform and not only pointwise. The rate of convergence is also established and an application to the numerical solution of singular integral equations is made.

[1]  P. Theocaris,et al.  On the numerical solution of singular integro-differential equations , 1979 .

[2]  F. Smithies,et al.  Singular Integral Equations , 1977 .

[3]  D. F. Paget,et al.  The numerical evaluation of Hadamard finite-part integrals , 1981 .

[4]  P. S. Theocaris,et al.  On the convergence of a Gauss quadrature rule for evaluation of Cauchy type singular integrals , 1977 .

[5]  Philip Rabinowitz,et al.  Methods of Numerical Integration , 1985 .

[6]  David Elliott,et al.  Gauss type quadrature rules for Cauchy principal value integrals , 1979 .

[7]  N. Ioakimidis.  Further convergence results for two quadrature rules for Cauchy type principal value integrals , 1982 .

[8]  David Elliott,et al.  An algorithm for the numerical evaluation of certain Cauchy principal value integrals , 1972 .

[9]  A. I. Kalandiya.  Mathematical Methods of Two-Dimensional Elasticity. , 1975 .

[10]  David Elliott,et al.  On the convergence of a quadrature rule for evaluating certain Cauchy principal value integrals , 1974 .

[11]  H. R. Kutt.  On the numerical evaluation of finite-part integrals involving an algebraic singularity , 1975 .

[12]  I. M. Longman.  On the numerical evaluation of Cauchy principal values of integrals. , 1958 .

[13]  David Elliott,et al.  On the convergence of Hunter's quadrature rule for Cauchy principal value integrals , 1979 .

[14]  D. Hunter,et al.  Some Gauss-type formulae for the evaluation of Cauchy principal values of integrals , 1972 .

[15]  Nikolaos I. Ioakimidis.  On the Numerical Evaluation of a Class of Finite‐Part Integrals , 1983 .

[16]  David Elliott,et al.  On the convergence of a quadrature rule for evaluating certain cauchy principal value integrals: An addendum , 1975 .