MODIFIED COMPOUND QUADRATURE-RULES FOR STRONGLY SINGULAR-INTEGRALS

被引：27

作者：

DIETHELM, K

机构：

[1] Institut für Mathematik, Universität Hildesheim, Hildesheim, D-31141

来源：

COMPUTING | 1994年 / 52卷 / 04期

关键词：

CAUCHY PRINCIPAL VALUE INTEGRALS; HADAMARD FINITE PART INTEGRALS; MODIFIED QUADRATURE FORMULA; MIDPOINT FORMULA; TRAPEZOIDAL FORMULA; SIMPSON FORMULA; PEANO CONSTANTS;

D O I：

10.1007/BF02276881

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We show that the error term of every modified compound quadrature rule for Cauchy principal value integrals with degree of exactness s is of optimal order of magnitude in the classes C(k)[-1, 1], k = 1, 2, ..., s, but not in C(s+1)[-1, 1]. We give explicit upper bounds for the error constants of the modified midpoint rule, the modified trapezoidal rule and the modified Simpson rule. Furthermore, the results are generalized to analogous rules for Hadamard-type finite part integrals.

引用

页码：337 / 354

页数：18

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