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

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

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주제분류수학

초록

Abstract

It is well known that the application of the nonlinear coordinatetransformations is useful for efficient numerical evaluation of weaklysingular integrals.In this paper, we consider the trapezoidal rule combined with a nonlineartransformation Omega_m(b;x), containing a parameter b, proposed first byYun cite{Yun1}.It is shown that the trapezoidal rule with the transformation Omega_m(b;x),like the case of the Gauss-Legendre quadrature rule, can improvethe asymptotic truncation error by using a moderately large b.By several examples, we compare the numerical results of the present methodwith those of some existing methods.This shows the superiority of the transformation Omega_m(b;x).

참고문헌 (15)

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