THE GALERKIN METHOD FOR SINGULAR INTEGRAL-EQUATIONS REVISITED

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:40

Article

VENTURINO, E

关键词: GALERKIN METHOD;    SINGULAR INTEGRAL EQUATIONS;   

DOI  :  10.1016/0377-0427(92)90044-X

来源: Elsevier

【 摘 要 】

In an earlier work, the author has obtained error bounds for the Galerkin method for solving Cauchy singular integral equations, discovering that the usually neglected constants contain the Riemann zeta function, when evaluated in the supremum norm. The aim of this investigation is twofold: to show that the occurrence of the Riemann zeta function in the error bound for the Chebyshev norm is sharp; and secondly to use this result to obtain a class of forcing functions for which the method does not yield an approximate solution differing from the analytical one by at most a prescribed error tolerance. These counterexamples indicate that in practical situations, for functions exhibiting a behavior similar to the one presented here, Galerkin's method might not lead to an acceptable solution.

【 授权许可】

Free