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We consider the general (composite) Newton-Cotes method for the computation of Cauchy principal value integrals and focus on its pointwise superconvergence phenomenon, which means that the rate of convergence of the Newton-Cotes quadrature rule is higher than what is globally possible when the singular point coincides with some a priori known point. The necessary and sufficient conditions satisfied by the superconvergence point are given. Moreover, the superconvergence estimate is obtained and the properties of the superconvergence points are investigated. Finally, some numerical examples are provided to validate the theoretical results.  相似文献
2.
In this paper, we present a general ellipsoidal artificial boundary method for three-dimensional exterior problem. The exact artificial boundary condition, which is expressed explicitly by the series concerning the ellipsoidal harmonic functions, is derived and then an equivalent problem in a bounded domain is presented. The error estimates show that the convergence rate depends on the mesh parameter, the number of terms used in the exact artificial boundary condition, and the location of the artificial boundary.  相似文献
3.
In this paper, the finite element method and the boundary element method are combined to solve numerically an exterior quasilinear elliptic problem. Based on an appropriate transformation and the Fourier series expansion, the exact quasilinear artificial boundary conditions and a series of the corresponding approximations for the given problem are presented. Then the original problem is reduced into an equivalent problem defined in a bounded computational domain. We provide error estimate for the Galerkin method. Numerical results are presented to illustrate the theoretical results.  相似文献
4.
The Clausen functions appear in many problems, such as in the computation of singular integrals, quantum field theory, and so on. In this paper, we consider the Clausen functions Cl n (θ) with n≥2. An efficient algorithm for evaluating them is suggested and the corresponding convergence analysis is established. Finally, some numerical examples are presented to show the efficiency of our algorithm.  相似文献
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