Computational and theoretical aspects of Romanovski-Bessel polynomials and their applications in spectral approximations
Zaky M.A. Abo-Gabal H. Hafez R.M. Doha E.H.
April 2022Springer
Numerical Algorithms
2022#89Issue 41567 - 1601 pp.
Our concern in this paper is with the essential properties of a finite class of orthogonal polynomials with respect to a weight function related to the probability density function of the inverse gamma distribution over the positive real line. We present some basic properties of the Romanovski-Bessel polynomials, the Romanovski-Bessel-Gauss-type quadrature formulae and the associated interpolation, discrete transforms, spectral differentiation and integration techniques in the physical and frequency spaces, and basic approximation results for the weighted projection operator in the nonuniformly weighted Sobolev space. We discuss the relationship between such kinds of finite orthogonal polynomials and other classes of finite and infinite orthogonal polynomials. Moreover, we propose adaptive spectral tau and collocation methods based on Romanovski-Bessel polynomial basis for solving linear and nonlinear high-order differential equations, respectively.
Finite orthogonal polynomials , Gauss-type quadrature , High-order differential equations , Romanovski-Bessel polynomials , Spectral methods
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Department of Applied Mathematics, Physics Division, National Research Centre, Dokki, Cairo, 12622, Egypt
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Department of Mathematics, Faculty of Science, Cairo University, Giza, 12613, Egypt
Faculty of Education, Matrouh University, Matrouh, Egypt
Department of Applied Mathematics
Institute of Mathematics and Mathematical Modeling
Department of Mathematics
Faculty of Education
10 лет помогаем публиковать статьи Международный издатель
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