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Efficient and Accurate Legendre Spectral Element Methods for One-Dimensional Higher Order Problems

, 2021
Efficient and accurate Legendre spectral element methods for solving onedimensional higher order differential equations with high oscillatory or steep gradient solutions are proposed.
Yang Zhang
semanticscholar   +1 more source

A Novel Spectral Method for Burgers Equation on The Real Line

East Asian Journal on Applied Mathematics, 2020
A spectral method for the Burgers equation on the whole real line based on generalised Hermite functions is proposed. The generalised stability and convergence of the method are proved.
Yu-jian Jiao
semanticscholar   +1 more source

Strictly positive definite kernels on the $2$-sphere: beyond radial symmetry

, 2020
The paper introduces a new characterisation of strict positive definiteness for kernels on the 2-sphere without assuming the kernel to be radially (isotropic) or axially symmetric. The results use the series expansion of the kernel in spherical harmonics.
Janin Jager
semanticscholar   +1 more source

A Legendre-Laguerre-Galerkin Method for Uniform Euler-Bernoulli Beam Equation

East Asian Journal on Applied Mathematics, 2018
We consider a Galerkin method based on Legendre and Laguerre polynomials and apply it to the Euler-Bernoulli beam equation. The matrices of the method are well structured, which results in substantial reduction of computational cost.
M. A. Bassuony   +3 more
semanticscholar   +1 more source

Integral representations and new generating functions of Chebyshev polynomials

, 2015
In this paper we use the two-variable Hermite polynomials and their operational rules to derive integral representations of Chebyshev polynomials. The concepts and the formalism of the Hermite polynomials Hn(x;y) are a powerful tool to obtain most of the
C. Cesarano
semanticscholar   +1 more source

Certain finite double integrals involving the hypergeometric function and Aleph-function

, 2016
The aim of this document is to evaluate four finite double integrals involving the product of two hypergeometric functions and the Alephfunction. At the end of this paper , we evaluate few particular cases. 2010 Mathematics Subject Classification: 33C05,
F. Ayant, D. Kumar
semanticscholar   +1 more source

Note on generating relations associated with the generalized Gauss hypergeometric function

, 2016
The objective of this paper is to establish some new generating relations involving the generalized hypergeometric function and the generalized confluent hypergeometric function by mainly applying Taylor’s theorem.
M. Chand, P. Agarwal, Junesang Choi
semanticscholar   +1 more source

A unified study of Fourier series involving the Aleph-function and the Kampé de Fériet's function

, 2016
: Recently Yashwant Singh et al [7] have studied Fourier series involving the I-function defined by V.P. Saxena [6]. Motivated by this work, we make an application of an integral involving sine function, exponential function, the product of Aleph ...
F. Ayant, D. Kumar
semanticscholar   +1 more source

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