The practical Gauss type rules for Hadamard finite-part integrals using Puiseux expansions

DOI10.1007/s10444-016-9487-7zbMath1373.65017OpenAlexW2530116259MaRDI QIDQ2400483

Tongke Wang, Zhi-Fang Liu, Zhi-Yue Zhang

Publication date: 1 September 2017

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10444-016-9487-7

zbMATH Keywords

numerical exampleasymptotic expansionquadrature formulaPuiseux expansionHadamard finite-part integralasymptotic expansion of the erroralgebraic and logarithmic singularitycomposite Gauss--Legendre quadrature rulecomposite Gauss-Kronrod quadrature rulegeneral composite quadrature formula

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items (8)

Uniform approximation to Cauchy principal value integrals with logarithmic singularity ⋮ Singular asymptotic expansion and Legendre collocation method for two-term weakly singular Volterra integral equation of the second kind ⋮ Singularity separation Chebyshev collocation method for weakly singular Volterra integral equations of the second kind ⋮ The asymptotic approximations to linear weakly singular Volterra integral equations via Laplace transform ⋮ An algorithm for the inversion of Laplace transforms using Puiseux expansions ⋮ The Puiseux expansion and numerical integration to nonlinear weakly singular Volterra integral equations of the second kind ⋮ The series expansion and Chebyshev collocation method for nonlinear singular two-point boundary value problems ⋮ FRACTIONAL HERMITE DEGENERATE KERNEL METHOD FOR LINEAR FREDHOLM INTEGRAL EQUATIONS INVOLVING ENDPOINT WEAK SINGULARITIES

Uses Software

• DLMF
• SInt

Cites Work

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