2020
DOI: 10.1186/s13662-020-02996-0
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Abstract: The present study is devoted to developing a computational collocation technique for solving the Cauchy singular integral equation of the second kind (CSIE-2). Although, several studies have investigated the numerical approximation solution of CSIEs, the strong singularity and accuracy of the numerical methods are still two important challenges for these integral equations. In this paper, we focus on the smooth transformation and implementation of Bessel basis polynomials (BBP). The reduction of the CSIEs-2 in… Show more

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Cited by 6 publications
(1 citation statement)
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“…Then the rate is improved to O(n −m ) [14] which now depends on m, but still at polynomial order. Some numerical methods for solving weakly singular equations are; Bessel polynomials via collocation method [15], Clenshaw-Curtis-Filon quadrature [16], Laguerre functions [17], B-spline Wavelet Galerkin method [18], Block-pulse functions [19], Lagrange interpolation with Gauss Legendre quadrature nodes [20]. In this work we assume that the…”
Section: Introductionmentioning
confidence: 99%
“…Then the rate is improved to O(n −m ) [14] which now depends on m, but still at polynomial order. Some numerical methods for solving weakly singular equations are; Bessel polynomials via collocation method [15], Clenshaw-Curtis-Filon quadrature [16], Laguerre functions [17], B-spline Wavelet Galerkin method [18], Block-pulse functions [19], Lagrange interpolation with Gauss Legendre quadrature nodes [20]. In this work we assume that the…”
Section: Introductionmentioning
confidence: 99%