Results 11 to 20 of about 53,539 (221)

An Efficient Numerical Scheme for Solving Multiorder Tempered Fractional Differential Equations via Operational Matrix

Journal of Mathematics, 2022
In this paper, we extend the operational matrix method to solve the tempered fractional differential equation, via shifted Legendre polynomial. Although the operational matrix method is widely used in solving various fractional calculus problems, it is ...
Abiodun Ezekiel Owoyemi, Chang Phang, Yoke Teng Toh   +2 more
doaj   +1 more source

Criterion for polynomial solutions to a class of linear differential equation of second order [PDF]

, 2006
We consider the differential equations y''=\lambda_0(x)y'+s_0(x)y, where \lambda_0(x), s_0(x) are C^{\infty}-functions. We prove (i) if the differential equation, has a polynomial solution of degree n >0, then \delta_n=\lambda_n s_{n-1}-\lambda_{n-1}s_n ...
Al-Salam W A, Barakat T, Barakat T, Bayrak O, Chihara T S, Ciftci H, Ciftci H, Erdélyi A, Fernández M F, Grünbaum F A, Hakan Ciftci, Littlejohn L L, Nasser Saad, Richard L Hall, Saad N, Turbiner A   +15 more
core   +1 more source

Comparison of Chebyshev and Legendre Polynomial Expansion of Phase Function of Cloud and Aerosol Particles

Advances in Meteorology, 2017
Chebyshev and Legendre polynomial expansion is used to reconstruct the Henyey-Greenstein phase function and the phase functions of spherical and nonspherical particles.
Feng Zhang, Kun Liu, Quan Yang, Kun Wu, Jian-Qi Zhao   +4 more
doaj   +1 more source

On computation of Hough functions [PDF]

Geoscientific Model Development, 2016
Hough functions are the eigenfunctions of the Laplace tidal equation governing fluid motion on a rotating sphere with a resting basic state. Several numerical methods have been used in the past.
H. Wang, J. P. Boyd, R. A. Akmaev
doaj   +1 more source

Genetic evaluation of European quails by random regression models

Revista Brasileira de Zootecnia, 2012
The objective of this study was to compare different random regression models, defined from different classes of heterogeneity of variance combined with different Legendre polynomial orders for the estimate of (co)variance of quails.
Flaviana Miranda Gonçalves, Aldrin Vieira Pires, Idalmo Garcia Pereira, Eduardo Silva Cordeiro Drumond, Vivian Paula Silva Felipe, Sandra Regina Freitas Pinheiro   +5 more
doaj   +1 more source

Legendre polynomial order selection in projection pursuit density estimation

Lietuvos Matematikos Rinkinys, 2013
Projection pursuit method and its application to probability density estimation is discussed. Method proposed by J.H. Friedman, based on projection density estimation using orthogonal Legendre polynomials, is analysed.
Mindaugas Kavaliauskas
doaj   +1 more source

The finite Fourier transform of classical polynomials [PDF]

, 2014
The finite Fourier transform of a family of orthogonal polynomials $A_{n}(x)$, is the usual transform of the polynomial extended by $0$ outside their natural domain.
Dixit, Atul, Jiu, Lin, Moll, Victor H., Vignat, Christophe   +3 more
core   +3 more sources

An Investigation into the Validity of the Temperature Profile Approximations across the Film Thickness in THD Analysis of Infinitely Wide Slider Bearing

Tribology Online, 2006
Many investigators have frequently assumed polynomial temperature profiles across the film thickness in the mathematical modeling of lubricating films in the hydrodynamic bearings in order to make computations simpler.
R. K. Sharma, R. K. Pandey
doaj   +1 more source

O(1) Computation of Legendre polynomials and Gauss-Legendre nodes and weights for parallel computing [PDF]

, 2012
A self-contained set of algorithms is proposed for the fast evaluation of Legendre polynomials of arbitrary degree and argument is an element of [-1, 1].
Bogaert, Ignace, Fostier, Jan, Michiels, Bart   +2 more
core   +1 more source

Properties of circumferential non-propagating waves in functionally graded piezoelectric cylindrical shells

Advances in Mechanical Engineering, 2019
Each guided elastic wave mode is composed of propagating and non-propagating branches. Non-propagating branches associated with complex wavenumbers are substantially different from the propagating ones.
Xiaoming Zhang, Zhi Li, Jiangong Yu, Bo Zhang   +3 more
doaj   +1 more source