Bernstein polynomials based iterative method for solving fractional integral equations

A novel iterative numerical method is constructed for solving second kind Volterra fractional integral equations. The method uses at each iterative step a Bernstein spline interpolation procedure combined with the corresponding quadrature formula. In this way, based on the nice approximation and sha...

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Bibliographic Details
Published inMathematica Slovaca Vol. 72; no. 6; pp. 1623 - 1640
Main Authors Satmari, Zoltan, Bica, Alexandru Mihai
Format Journal Article
LanguageEnglish
Published Heidelberg De Gruyter 16.12.2022
Walter de Gruyter GmbH
Subjects
65R20
Bernstein polynomials
Fractional calculus
Fractional integral equation
Integral equations
Interpolation
Iterative methods
iterative numerical method
Mathematical analysis
Numerical methods
Polynomials
Primary 65R20
Quadratures
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Summary:A novel iterative numerical method is constructed for solving second kind Volterra fractional integral equations. The method uses at each iterative step a Bernstein spline interpolation procedure combined with the corresponding quadrature formula. In this way, based on the nice approximation and shape preserving properties of the Bernstein polynomials, we propose an alternative to the classical product integration technique that uses trapezoidal, Simpson, Gauss type and other well-known quadrature formulas. The convergence of the method is proved with the error estimate expressed in terms of the Lipschitz constants and the accuracy is illustrated on some numerical experiments.
ISSN:0139-9918
1337-2211
DOI:10.1515/ms-2022-0112