Some applications of the Stirling numbers of the first and second kind

DOI10.1007/S12190-014-0767-4zbMath1318.65014OpenAlexW2065100708MaRDI QIDQ2354193

Yanyan Li

Publication date: 10 July 2015

Published in: Journal of Applied Mathematics and Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12190-014-0767-4

zbMATH Keywords

numerical exampleFredholm integral equationsStirling numbersNewton interpolationexplicit forms of the Adams-Bashforth and Adams-Moulton rulesexplicit forms of the weighted Newton-Cotes integration formulas

Mathematics Subject Classification ID

Bell and Stirling numbers (11B73) Numerical methods for integral equations (65R20) Linear ordinary differential equations and systems (34A30) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Fredholm integral equations (45B05) Analytic computations (11Y35)

Related Items (1)

An extension of the Taylor series expansion by using the Bell polynomials

Cites Work

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• Explicit forms of weighted quadrature rules with geometric nodes
• Nonstandard Gaussian quadrature formulae based on operator values
• Newton--Cotes formulae for long-time integration.
• Some families of generating functions associated with the Stirling numbers of the second kind
• Gaussian quadrature rules using function derivatives
• Interpolation Processes
• On Stirling Functions of the Second Kind
• Closed expressions for coefficients in weighted Newton-Cotes quadratures
• Numerical Methods for Ordinary Differential Equations

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