Quadrature rule for indefinite integral of algebraic–logarithmic singular integrands
Copyright policy )Quadrature rule for indefinite integral of algebraic–logarithmic singular integrands
The authors present an automatic quadrature method to approximate the indefinite integral of functions involving algebraic-logarithmic singularities. The computation of such integrals is required to solve some integral equations derived from the Schrödinger equation in nuclear physics. The present scheme is an extension of the Clenshaw-Curtis method [cf. \textit{C. W. Clenshaw} and \textit{A. R. Curtis}, Numer. Math. 2, 197--205 (1960; Zbl 0093.14006)], where the smooth part of the integrand function is interpolated by a sum of the Chebyshev polynomials of the first kind. The indefinite integral is uniformly approximated and an estimation of the error of the quadrature rule is given. Finally numerical examples on several test integrals and a comparison with a subroutine of QUADPACK are provided and show the performance of the present quadrature scheme.
- University of Fukui Japan
- Nanzan University Japan
integral equations, numerical examples, Applied Mathematics, indefinite integral, quadrature rule, Schrödinger equation, Numerical methods for integral equations, Clenshaw-Curtis method, Numerical quadrature and cubature formulas, Approximate quadratures, algebraic-logarithmic singularity, Uniform approximation, Computational Mathematics, Indefinite integral, uniform approximation, Error analysis, Algebraic–logarithmic singularity, Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics, Quadrature rule, error analysis
integral equations, numerical examples, Applied Mathematics, indefinite integral, quadrature rule, Schrödinger equation, Numerical methods for integral equations, Clenshaw-Curtis method, Numerical quadrature and cubature formulas, Approximate quadratures, algebraic-logarithmic singularity, Uniform approximation, Computational Mathematics, Indefinite integral, uniform approximation, Error analysis, Algebraic–logarithmic singularity, Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics, Quadrature rule, error analysis
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