On Gauss-Type Quadrature Rules

Some orthogonal polynomials on the finite interval and Gaussian quadrature rules for fractional Riemann‐Liouville integrals

“…With the inspiration from the papers, 15,16,17 we studied some classes of orthogonal polynomials on finite intervals and derived the corresponding quadrature formulas of Gaussian type, which can be successfully applied in numerical calculation of the left and right fractional Riemann-Liouville integrals, providing two main statements.…”

“…Bokhari, Qadir, and Al-Attas 15 considered Gauss quadrature rules, as well as Gauss-Radau and Gauss-Lobatto rules, based on polynomials p n (t) orthogonal on (0, 1) with respect to the linear weight function (t) ∶ = 1 − t. The authors discussed a development of the corresponding orthogonal polynomials p n (t) via Gaussian hypergeometric differential equation, narrated some of its properties, derived the three-term recurrence relation for the monic polynomials (see theorem 2 in Rainville 15 )…”

“…The alternative package SOPQ in Matlab was developed by Gautschi. 10,14 Inspired by the recent papers, 15,16,17 in this paper, we consider certain classes of orthogonal polynomials on the finite intervals and derive the corresponding quadrature formulas of the maximal algebraic degree of precision, which can be successfully applied in numerical calculation of the left and right fractional Riemann-Liouville integrals (cf. 18,19,20,21 ) 5) respectively, as well as their multiple composition, recently introduced in Ciesielski and Blaszczyk.…”

“…In Section 2, we analyze results from Bokhari et al 15 and Milovanović 16 and consider the generalized case with the weight function…”

Perbandingan Metode Gauss- Legendre, Gauss-Lobatto, dan Gauss-Kronrod pada Integrasi Numerik Fungsi Eksponensial

“…Konsep dasar metode ini yaitu menghitung nilai integral dengan cara mengambil nilai fungsi di beberapa titik tertentu (fixed point) yang disebut dengan titik evaluasi dan mengalikan dengan fungsi pembobot integrasi (Bokhari, 2009 …”