Results 21 to 30 of about 44,437 (210)
A numerical method for distributed-order time fractional 2D Sobolev equation
Results in Physics, 2023 In this work, the distributed-order time fractional 2D Sobolev equation is introduced. The orthonormal Bernoulli polynomials, as a renowned family of basis functions, are employed to solve this problem.
M.H. Heydari, S. Rashid, F. Jarad
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Advances in Difference Equations, 2021 This paper applies the Heydari–Hosseininia nonsingular fractional derivative for defining a variable-order fractional version of the Sobolev equation. The orthonormal shifted discrete Legendre polynomials, as an appropriate family of basis functions, are
M. H. Heydari, A. Atangana
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Using shifted Legendre orthonormal polynomials for solving fractional optimal control problems [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2022 shifted Legendre orthonormal polynomials (SLOPs) are used to approximate the numerical solutions of fractional optimal control problems. To do so, first, the operational matrix of the Caputo fractional derivative, the SLOPs, and Lagrange ...
R. Naseri, A. Heydari, A.S. Bagherzadeh
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Uniformly bounded orthonormal polynomials on the sphere [PDF]
Bulletin of the London Mathematical Society, 2015 Improved presentation and corrected ...
Marzo Sánchez, Jordi +1 more
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Approximation of functions in Hölder’s class and solution of nonlinear Lane–Emden differential equation by orthonormal Euler wavelets [PDF]
Iranian Journal of Numerical Analysis and OptimizationIn this article, a method has been developed for the solution of a non-linear Lane-Emden differential equation based on orthonormal Euler wavelet series.
H.C. Yadav, A. Yadav, S. Lal
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Derivatives of Integrating Functions for Orthonormal Polynomials with Exponential-Type Weights
Journal of Inequalities and Applications, 2009 Let wρ(x):=|x|ρexp(−Q(x)), ρ>−1/2, where Q∈C2:(−∞,∞)→[0,∞) is an even function.
Hee Sun Jung, Ryozi Sakai
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Stable Calculation of Krawtchouk Functions from Triplet Relations
Mathematics, 2021 Deployment of the recurrence relation or difference equation to generate discrete classical orthogonal polynomials is vulnerable to error propagation. This issue is addressed for the case of Krawtchouk functions, i.e., the orthonormal basis derived from ...
Albertus C. den Brinker
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New Operational Matrices of Seventh Degree Orthonormal Bernstein Polynomials
مجلة بغداد للعلوم, 2015 Based on analyzing the properties of Bernstein polynomials, the extended orthonormal Bernstein polynomials, defined on the interval [0, 1] for n=7 is achieved. Another method for computing operational matrices of derivative and integration D_b and R_(n+1)
Baghdad Science Journal
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Useful Bases for Problems in Nuclear and Particle Physics [PDF]
, 1996 A set of exactly computable orthonormal basis functions that are useful in computations involving constituent quarks is presented. These basis functions are distinguished by the property that they fall off algebraically in momentum space and can be ...
Abramowitz +16 more
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Calculating Bivariate Orthonormal Polynomials By Recurrence
Australian & New Zealand Journal of Statistics, 2013 SummaryEmerson gave recurrence formulae for the calculation of orthonormal polynomials for univariate discrete random variables. He claimed that as these were based on the Christoffel–Darboux recurrence relation they were more efficient than those based on the Gram–Schmidt method.
Rayner, J. C. W. +3 more
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