The asymptotic expansion and extrapolation of trapezoidal rule for integrals with fractional order singularities
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Publication:5259059
DOI10.1080/00207160.2014.902447zbMath1317.65066OpenAlexW2039991802MaRDI QIDQ5259059
Tongke Wang, Na Li, Guang-hua Gao
Publication date: 24 June 2015
Published in: International Journal of Computer Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1080/00207160.2014.902447
singular integrallocal fractional derivativeerror asymptotic expansionfractional Taylor's expansionmodified Romberg methodtrapezoidal integration formula
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Cites Work
- Extrapolation methods in numerical integration
- On calculus of local fractional derivatives
- The generalization of Faulhaber's formula to sums of non-integral powers
- Generalized Taylor's formula
- On the local fractional derivative
- On a Riemann-Liouville generalized Taylor's formula
- Euler-Maclaurin expansions for integrals with endpoint singularities: A new perspective
- Some integral and asymptotic formulas associated with the Hurwitz zeta function
- Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable. functions. Further results
- Euler–Maclaurin expansions for integrals with arbitrary algebraic endpoint singularities
- A review of error estimation in adaptive quadrature
- Functional Fractional Calculus
- An Extension of the Euler-Maclaurin Summation Formula to Functions with a Branch Singularity
- An extrapolation procedure for the evaluation of singular integrals
- A Further Extension of the Euler-Maclaurin Summation Formula
- Practical Extrapolation Methods
- Fractional differentiability of nowhere differentiable functions and dimensions
- The Riemann zeta-function and its derivatives
- Romberg integration for a class of singular integrands
- On the Definite Integration of Singular Integrands
- Numerical Integration of Non‐analytic Functions
- Survey of Extrapolation Processes in Numerical Analysis
- About non-differentiable functions
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