On representation of a solution to the Cauchy problem by a Fourier series in Sobolev-orthogonal polynomials generated by Laguerre polynomials

DOI10.1134/S0012266118010068zbMath1398.42015OpenAlexW2800437628MaRDI QIDQ1649467

I. I. Sharapudinov, M. G. Magomed-Kasumov

Publication date: 6 July 2018

Published in: Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0012266118010068

zbMATH Keywords

error estimatesuniform convergenceCauchy problemspectral methodsclassical orthogonal Laguerre polynomialsFourier-Sobolev expansionsSobolev inner products and orthogonal polynomials

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05)

Related Items (8)

Approximation properties of the Vallée-Poussin means similar to the partial sums of Fourier series in Laguerre-Sobolev polynomials ⋮ Sobolev orthogonal polynomials associated with Chebyshev polynomials of the first kind and the Cauchy problem for ordinary differential equations ⋮ On the approximative properties of Fourier series in Laguerre-Sobolev polynomials ⋮ On the Uniform Convergence of the Fourier Series by the System of Polynomials Generated by the System of Laguerre Polynomials ⋮ Sobolev-orthogonal systems of functions and the Cauchy problem for ODEs ⋮ Sobolev-Orthonormal System of Functions Generated by the System of Laguerre Functions ⋮ Sobolev-orthogonal systems of functions and some of their applications ⋮ Recurrence Relations for Polynomials Orthonormal on Sobolev, Generated by Laguerre Polynomials

Uses Software

• Matlab

Cites Work

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• Spectral Methods in MATLAB
• Approximation of functions of variable smoothness by Fourier-Legendre sums
• Mean Convergence of Expansions in Laguerre and Hermite Series
• Approximation properties of mixed series in terms of Legendre polynomials on the classes $ {W^r}$

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