Results 41 to 50 of about 1,811 (151)
Advances in Difference Equations, 2021 In this work, a technique for finding approximate solutions for ordinary fraction differential equations (OFDEs) of any order has been proposed. The method is a hybrid between Galerkin and collocation methods.
Mohamed Abdelhakem +3 more
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Spectral Analysis of Certain Schr\"odinger Operators [PDF]
, 2012 The $J$-matrix method is extended to difference and $q$-difference operators and is applied to several explicit differential, difference, $q$-difference and second order Askey-Wilson type operators. The spectrum and the spectral measures are discussed in
Ismail, Mourad E. H., Koelink, Erik
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Studies in Applied Mathematics, Volume 145, Issue 1, Page 3-35, July 2020., 2020 Abstract Sparse spectral methods for solving partial differential equations have been derived in recent years using hierarchies of classical orthogonal polynomials on intervals, disks, and triangles. In this work, we extend this methodology to a hierarchy of nonclassical orthogonal polynomials on disk slices and trapeziums.
Ben Snowball, Sheehan Olver
wiley +1 more source
Bilateral generating functions for a new class of generalized Legendre polynominals
International Journal of Mathematics and Mathematical Sciences, 1980 Recently Chatterjea (1) has proved a theorem to deduce a bilateral generating function for the Ultraspherical polynomials. In the present paper an attempt has been made to give a general version of Chatterjea's theorem.
A. N. Srivastava +2 more
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The automatic solution of partial differential equations using a global spectral method [PDF]
, 2015 A spectral method for solving linear partial differential equations (PDEs) with variable coefficients and general boundary conditions defined on rectangular domains is described, based on separable representations of partial differential operators and ...
Olver, Sheehan, Townsend, Alex
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Mathematical Problems in Engineering, Volume 2020, Issue 1, 2020., 2020 In this paper, we obtain some generating matrix functions and integral representations for the extended Gauss hypergeometric matrix function EGHMF and their special cases are also given. Furthermore, a specific application for the extended Gauss hypergeometric matrix function which includes Jacobi matrix polynomials is constructed.
Fuli He +4 more
wiley +1 more source
On the Complex Zeros of Some Families of Orthogonal Polynomials
Abstract and Applied Analysis, 2010 The complex zeros of the orthogonal Laguerre polynomials 𝐿𝑛(𝑎)(𝑥) for ...
Eugenia N. Petropoulou
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A new characterization of ultraspherical polynomials [PDF]
Proceedings of the American Mathematical Society, 2008 We characterize the class of ultraspherical polynomials in between all symmetric orthogonal polynomials on [-1,1] via the special form of the representation of the derivatives p' n+1 (x) by p k (x), k = 0,..., n.
R. Lasser, J. Obermaier
openaire +1 more source
The Algebra of Differential Operators for a Gegenbauer Weight Matrix [PDF]
, 2015 In this paper we study in detail algebraic properties of the algebra $\mathcal D(W)$ of differential operators associated to a matrix weight of Gegenbauer type.
Zurrián, Ignacio
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Complex and distributional weights for sieved ultraspherical polynomials
International Journal of Mathematics and Mathematical Sciences, 1996 Contour integral and distributional orthogonality of sieved ultraspherical polynomials are established for values of the parameters outside the natural range of orthogonality by positive measures on the real line.
Jairo A. Charris, Felix H. Soriano
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