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The trapezoidal rule with a nonlinear coordinate transformation for weakly singular integrals

윤병인
대한수학회 (The Korean Mathematical Society)|2004.11|대한수학회지 (Journal of the KMS)|제41권 제6호|pp. 957-976

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참고문헌

주제분류수학

초록

Abstract

It is well known that the application of the nonlinear coordinate transformations is useful for efficient numerical evaluation of weakly singular integrals. In this paper, we consider the trapezoidal rule combined with a nonlinear transformation Ωm(b; x), containing a parameter b, proposed first by Yun [14]. It is shown that the trapezoidal rule with the transformation Ωm(b; x), like the case of the Gauss-Legendre quadrature rule, can improve the asymptotic truncation error by using a moderately large b. By several examples, we compare the numerical results of the present method with those of some existing methods. This shows the superiority of the transformation Ωm(b; x).

참고문헌 (13)

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