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Applicable Analysis
An International Journal
Volume 1, 1971 - Issue 3
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Original Articles

Estimation of errors in the numerical quadrature of analytic functions

Hidetosi Takahasi Computer Centre, University of Tokyo, Bunkyo-ku, Tokyo, Japan
&
Masatake Mori Research Institute for Mathematical Sciences, Kyoto University, Kitashirakawa, Kyoto, Japan
Pages 201-229 | Published online: 10 May 2007

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Ikuo Suzuki & Yoshihiro Ishibashi. (1985) The structure, the formation energy and the activation energy of domain walls in ferroelectrics. Ferroelectrics 64:1, pages 181-187.
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Articles from other publishers (23)

Lloyd N. Trefethen, Yuji Nakatsukasa & J. A. C. Weideman. (2021) Exponential node clustering at singularities for rational approximation, quadrature, and PDEs. Numerische Mathematik 147:1, pages 227-254.
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Yoshihiro Ishibashi & Makoto Iwata. (2020) Activation Energy of Ferroelectric Domain Wall. Journal of the Physical Society of Japan 89:1, pages 014705.
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Hassan Majidian. (2018) Stable application of Filon–Clenshaw–Curtis rules to singular oscillatory integrals by exponential transformations. BIT Numerical Mathematics 59:1, pages 155-181.
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J. A. C. Weideman. (2019) Gauss--Hermite Quadrature for the Bromwich Integral. SIAM Journal on Numerical Analysis 57:5, pages 2200-2216.
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Richard Mikael Slevinsky & Sheehan Olver. (2015) On The Use of Conformal Maps for the Acceleration of Convergence of the Trapezoidal Rule and Sinc Numerical Methods. SIAM Journal on Scientific Computing 37:2, pages A676-A700.
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Ioannis D. Koufogiannis, Michael Mattes & Juan R. Mosig. (2015) On the Development and Evaluation of Spatial-Domain Green’s Functions for Multilayered Structures With Conductive Sheets. IEEE Transactions on Microwave Theory and Techniques 63:1, pages 20-29.
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Mohsin Javed & Lloyd N. Trefethen. (2014) A trapezoidal rule error bound unifying the Euler–Maclaurin formula and geometric convergence for periodic functions. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470:2161, pages 20130571.
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Lloyd N. Trefethen & J. A. C. Weideman. (2014) The Exponentially Convergent Trapezoidal Rule. SIAM Review 56:3, pages 385-458.
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Nico M. Temme. (2009) The leaky aquifer function revisited. International Journal of Quantum Chemistry 109:13, pages 2826-2830.
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Lloyd N. Trefethen. (2008) Is Gauss Quadrature Better than Clenshaw–Curtis?. SIAM Review 50:1, pages 67-87.
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J. A. C. Weideman & L. N. Trefethen. (2007) The kink phenomenon in Fejér and Clenshaw–Curtis quadrature. Numerische Mathematik 107:4, pages 707-727.
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Prem Kythe & Michael Schäferkotter. 2004. Handbook of Computational Methods for Integration. Handbook of Computational Methods for Integration 551 583 .
Walter Gautschi. 1992. Numerical Integration. Numerical Integration 133 145 .
Qazi I. Rahman & Gerhard Schmeisser. (1990) Quadrature formulae and functions of exponential type. Mathematics of Computation 54:189, pages 245-270.
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Yoshihiro Ishibashi & Ikuo Suzuki. (1984) On the Evaluation of the Pinning (Peierls) Energy of Kinks Due to Discreteness of Substrate Lattices. Journal of the Physical Society of Japan 53:12, pages 4250-4256.
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Yoshihiro Ishibashi & Ikuo Suzuki. (1984) On the Peierls Energy of a Dislocation Describable in Terms of a Double-Sine-Gordon Equation. Journal of the Physical Society of Japan 53:4, pages 1366-1370.
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G. Monegato. (1982) The numerical evaluation of one-dimensional Cauchy principal value integralsDie numerische Bestimmung der eindimensionalen Cauchyschen Hauptwertintegralen. Computing 29:4, pages 337-354.
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Walter Gautschi. 1981. E. B. Christoffel. E. B. Christoffel 72 147 .
N.I. Ioakimidis & P.S. Theocaris. (1980) On the selection of collocation points for the numerical solution of singular integral equations with generalized kernels appearing in elasticity problems. Computers & Structures 11:4, pages 289-295.
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Yoshihiro Ishibashi. (1979) Computational Method of Activation Energy of Thick Domain Walls. Journal of the Physical Society of Japan 46:4, pages 1254-1257.
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Frank G. Lether. (1977) Modified quadrature formulas for functions with nearby poles. Journal of Computational and Applied Mathematics 3:1, pages 3-9.
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N.I. Ioakimidis & P.S. Theocaris. (1977) The gauss-hermite numerical integration method for the solution of the plane elastic problem of semi-infinite periodic cracks. International Journal of Engineering Science 15:4, pages 271-280.
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Hidetosi Takahasi & Masatake Mori. (1973) Quadrature formulas obtained by variable transformation. Numerische Mathematik 21:3, pages 206-219.
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