On using third and fourth kinds Chebyshev polynomials for solving the integrated forms of high odd-order linear boundary value problems

DOI10.1016/J.JOEMS.2014.04.008zbMath1327.65196OpenAlexW1990348053MaRDI QIDQ895201

M. M. Alsuyuti, Waleed M. Abd-Elhameed, Eid H. Doha

Publication date: 26 November 2015

Published in: Journal of the Egyptian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.joems.2014.04.008

zbMATH Keywords

integrated formsChebyshev polynomials of third and fourth kindsdual Petrov-Galerkin methodhigh odd-order two points boundary value problems

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Series solutions to PDEs (35C10) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items (7)

Expressing sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials by several orthogonal polynomials ⋮ Sums of finite products of Chebyshev polynomials of the third and fourth kinds ⋮ Some properties of the pseudo-Chebyshev polynomials of half-integer degree ⋮ The third and fourth kind pseudo-Chebyshev polynomials of half-integer degree ⋮ Connection problem for sums of finite products of Chebyshev polynomials of the third and fourth kinds ⋮ Complex spirals and pseudo-Chebyshev polynomials of fractional degree ⋮ Representation by Chebyshev polynomials for sums of finite products of Chebyshev polynomials

Cites Work

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• Efficient spectral-Petrov-Galerkin methods for the integrated forms of third- and fifth-order elliptic differential equations using general parameters generalized Jacobi polynomials
• An \(O(h^6)\) numerical solution of general nonlinear fifth-order two point boundary value problems
• Efficient spectral Legendre dual-Petrov-Galerkin algorithms for the direct solution of \((2n+1)\)th-order linear differential equations
• The numerical solution of fifth-order boundary value problems by the variational iteration method
• Efficient multi-dimensional solution of PDEs using Chebyshev spectral methods
• Chebyshev polynomials of the second, third and fourth kinds in approximation, indefinite integration, and integral transforms
• Existence of positive solutions to a singular second order boundary value problem
• The numerical solution of fifth-order boundary value problems with sixth-degree B-spline functions
• The third and fourth kinds of Chebyshev polynomials and best uniform approximation
• New wavelets collocation method for solving second-order multipoint boundary value problems using Chebyshev polynomials of third and fourth kinds
• On the coefficients of integrated expansions and integrals of Chebyshev polynomials of third and fourth kinds
• Efficient spectral ultraspherical-dual-Petrov-Galerkin algorithms for the direct solution of \((2n + 1)\)th-order linear differential equations
• New algorithms for solving high even-order differential equations using third and fourth Chebyshev-Galerkin methods
• Efficient spectral-Petrov-Galerkin methods for third- and fifth-order differential equations using general parameters generalized Jacobi polynomials
• Quartic spline solution of a third order singularly perturbed boundary value problem
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• Spectral Galerkin methods for the primary two-point boundary value problem in modelling viscoelastic flows
• Spectral collocation methods for the primary two-point boundary value problem in modelling viscoelastic flows
• Singular perturbations and differential inequalities
• The numerical solution of fifth-order boundary value problems by the decomposition method
• Rational Chebyshev spectral methods for unbounded solutions on an infinite interval using polynomial-growth special basis functions

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