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International Journal of Computer Mathematics Volume 6, 1977 - Issue 3
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Original Articles

Extension of numerical quadrature formulae to cater for end point singular behaviours over finite intervals

C. G. Harris Physics Laboratories, University of Kent at Canterbury, Canterbury, Kent, CT2 7NR, U.K.
&
W. A. B. Evans Physics Laboratories, University of Kent at Canterbury, Canterbury, Kent, CT2 7NR, U.K.
Pages 219-227 | Published online: 19 Mar 2007

Citations (33)

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Read on this site (5)

Eleni G. Anastasselou. (1984) Computation of the roots of cauchy type principal value integrals. International Journal of Computer Mathematics 16:2, pages 85-96.
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G.A. Evans, R.C. Forbes & J. Hyslop. (1984) The tanh transformation for singular integrals. International Journal of Computer Mathematics 15:1-4, pages 339-358.
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G.A. Evans, R.C. Forbes & J. Hyslop. (1983) Polynomial transformations for singular integrals. International Journal of Computer Mathematics 14:2, pages 157-170.
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G. A. Evans, J. Hyslop & A. P. G. Morgan. (1983) An extrapolation procedure for the evaluation of singular integrals. International Journal of Computer Mathematics 12:3-4, pages 251-265.
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William Squire. (1979) A comment on quadrature in the presence of end point singularities. International Journal of Computer Mathematics 7:3, pages 239-241.
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Articles from other publishers (28)

Gradimir V. Milovanović, Tomislav S. Igić & Dragana Turnić. (2015) Generalized quadrature rules of Gaussian type for numerical evaluation of singular integrals. Journal of Computational and Applied Mathematics 278, pages 306-325.
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Qiang Chen, Weihua Li & Jiangtao Wu. (2014) Realization of a multipath ultrasonic gas flowmeter based on transit-time technique. Ultrasonics 54:1, pages 285-290.
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W. A. B. Evans & A. Torre. (2012) On numerical integration with high-order quadratures: with application to the Rayleigh–Sommerfeld integral. Applied Physics B 109:2, pages 295-309.
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Daan Huybrechs & Ronald Cools. (2009) On Generalized Gaussian Quadrature Rules for Singular and Nearly Singular Integrals. SIAM Journal on Numerical Analysis 47:1, pages 719-739.
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Gradimir V. Milovanovic & Aleksandar S. Cvetkovic. (2005) Gaussian-type Quadrature Rules for Müntz Systems. SIAM Journal on Scientific Computing 27:3, pages 893-913.
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Prem Kythe & Michael Schäferkotter. 2004. Handbook of Computational Methods for Integration. Handbook of Computational Methods for Integration 551 583 .
Gradimir V. Milovanović. 1999. Applications and Computation of Orthogonal Polynomials. Applications and Computation of Orthogonal Polynomials 179 194 .
W. A. B. Evans & M. J. Ford. (1996) An integral equation approach to internal (2-layer) solitary waves. Physics of Fluids 8:8, pages 2032-2047.
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G. Burgess & E. Mahajerin. (1996) Accurate body force integration in boundary methods applied to plane elasticity. Computers & Structures 60:3, pages 411-414.
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. (1997) An exact integral equation for solitary waves (with new numerical results for some ‘internal’ properties). Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 452:1945, pages 373-390.
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Edward F. Kuester. (1995) Computable error bounds for variational functionals of solutions of a convolution integral equations of the first kind. Wave Motion 22:2, pages 171-185.
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I-Fan Shen, W. J. Easson, C. A. Greated & W. A. B. Evans. (1994) The modulation of short waves riding on solitary waves. Physics of Fluids 6:10, pages 3317-3323.
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John A. Crow. (1993) Quadrature of integrands with a logarithmic singularity. Mathematics of Computation 60:201, pages 297-301.
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Z. Heng & D. McCammond. (1992) An improved numerical integration technique for boundary integral evaluation in anisotropic plate problems. Computer Methods in Applied Mechanics and Engineering 97:3, pages 317-320.
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Jacobo Bielak, Richard C. MacCamy, David S. McGhee & Ahmadou Barry. (1991) Unified Symmetric BEM‐FEM for Site Effects on Ground Motion—SH Waves. Journal of Engineering Mechanics 117:10, pages 2265-2285.
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C.N. Pannell, W.A.B. Evans & D.A. Jackson. (1990) A new integration technique for flowmeters with chordal paths. Flow Measurement and Instrumentation 1:4, pages 216-224.
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Z. Heng. (2005) Boundary element study of an anisotropic plate. Communications in Applied Numerical Methods 4:4, pages 557-559.
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J G Powles, M L Williams & W A B Evans. (1988) Does a microscopically inhomogenous polar liquid have a dielectric constant?. Journal of Physics C: Solid State Physics 21:8, pages 1639-1659.
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Nikolaos I. Ioakimidis. (1988) A unified Riemann-Hilbert approach to the analytical determination of zeros of sectionally analytic functions. Journal of Mathematical Analysis and Applications 129:1, pages 134-141.
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Nikolaos I. Ioakimidis. 1987. Numerical Integration. Numerical Integration 61 82 .
Enayat Mahajerin & David L. Sikarskie. (2016) Boundary Element Study of a Loaded Hole in an Orthotropic Plate. Journal of Composite Materials 20:4, pages 375-389.
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J. Bielak & R.C. MacCamy. 1984. Unification of Finite Element Methods. Unification of Finite Element Methods 149 165 .
D MacGowan. (1982) Systematic graphical correction of the hypernetted chain theory for the one-component plasma. Journal of Physics A: Mathematical and General 15:3, pages 1007-1028.
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J V Ashby. (1981) Detailed solutions for non-equilibrium superconductivity. II. Multiple gap states. Journal of Physics F: Metal Physics 11:12, pages 2623-2631.
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J V Ashby & G Rickayzen. (1981) Detailed solutions for non-equilibrium superconductivity. I. Temperature-dependent solutions. Journal of Physics F: Metal Physics 11:12, pages 2595-2622.
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Duong Dang Do & Paul F. Greenfield. (1981) A finite integral transform technique for solving the diffusion-reaction equation with Michaelis-Menten kinetics. Mathematical Biosciences 54:1-2, pages 31-47.
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William Squire. (1981) In defense of linear quadrature rules. Computers & Mathematics with Applications 7:2, pages 147-149.
Crossref
Walter Gautschi. 1981. E. B. Christoffel. E. B. Christoffel 72 147 .

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