We consider the computation of the. Cauchy principal value mtegral by quadrature formulaeof compound type, which are obtained by replacing f by a piecewise defined function F,[;]. The behaviour of the constants m the ...We consider the computation of the. Cauchy principal value mtegral by quadrature formulaeof compound type, which are obtained by replacing f by a piecewise defined function F,[;]. The behaviour of the constants m the estimates where quadrature error) is determined for fixed i and which means that not only the. order, but also the coefficient of the main term of is determined. The behaviour of these error constants is compared -with the corresponding ones obtained for the. method of subtraction of the singularity. As it turns out, these error constants have, in general, the same asymptotic behaviour.展开更多
The classical composite rectangle (constant) rule for the computation of Cauchy principle value integral with the singular kernel is discussed. We show that the superconvergence rate of the composite midpoint ru...The classical composite rectangle (constant) rule for the computation of Cauchy principle value integral with the singular kernel is discussed. We show that the superconvergence rate of the composite midpoint rule occurs at certain local coodinate of each subinterval and obtain the corresponding superconvergence error estimate. Then collation methods are presented to solve certain kind of Hilbert singular integral equation. At last, some numerical examples are provided to validate the theoretical analysis.展开更多
The Peano derivatives are introduced for functions along an arc in the complex plane. Singular integrals of arbitrary order with singularities at its end-points are defined so that a unified theory for such integrals ...The Peano derivatives are introduced for functions along an arc in the complex plane. Singular integrals of arbitrary order with singularities at its end-points are defined so that a unified theory for such integrals and Cauchy principal value integrals is established.展开更多
Focuses on a study that proposed product formulas based on projector-splines for the numerical evaluation of two-dimensional Cauchy principal value integrals. Preliminaries; Convergence of quadrature rules using proje...Focuses on a study that proposed product formulas based on projector-splines for the numerical evaluation of two-dimensional Cauchy principal value integrals. Preliminaries; Convergence of quadrature rules using projector-splines; Numerical results.展开更多
文摘We consider the computation of the. Cauchy principal value mtegral by quadrature formulaeof compound type, which are obtained by replacing f by a piecewise defined function F,[;]. The behaviour of the constants m the estimates where quadrature error) is determined for fixed i and which means that not only the. order, but also the coefficient of the main term of is determined. The behaviour of these error constants is compared -with the corresponding ones obtained for the. method of subtraction of the singularity. As it turns out, these error constants have, in general, the same asymptotic behaviour.
文摘The classical composite rectangle (constant) rule for the computation of Cauchy principle value integral with the singular kernel is discussed. We show that the superconvergence rate of the composite midpoint rule occurs at certain local coodinate of each subinterval and obtain the corresponding superconvergence error estimate. Then collation methods are presented to solve certain kind of Hilbert singular integral equation. At last, some numerical examples are provided to validate the theoretical analysis.
文摘The Peano derivatives are introduced for functions along an arc in the complex plane. Singular integrals of arbitrary order with singularities at its end-points are defined so that a unified theory for such integrals and Cauchy principal value integrals is established.
基金Work sponsored by M.U.R.S.T. and C.N.R. of Italy.
文摘Focuses on a study that proposed product formulas based on projector-splines for the numerical evaluation of two-dimensional Cauchy principal value integrals. Preliminaries; Convergence of quadrature rules using projector-splines; Numerical results.
