Approximation properties of the q-sine bases

Lyonell Boulton; Gabriel Lord

doi:10.1098/rspa.2010.0486

Approximation properties of the q-sine bases

Lyonell Boulton, Gabriel Lord

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

For q >= 12/11, the eigenfunctions of the nonlinear eigenvalue problem associated with the one-dimensional q-Laplacian are known to form a Riesz basis of L-2(0, 1). We examine in this paper the approximation properties of this family of functions and its dual, and establish a non-orthogonal spectral method for the p-poisson boundary value problem and its corresponding parabolic time-evolution initial value problem with stochastic forcing. The principal objective of our analysis is the determination of optimal values of q for which the best approximation is achieved for a given p problem.

Original language	English
Pages (from-to)	2690-2711
Number of pages	22
Journal	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	467
Issue number	2133
DOIs	https://doi.org/10.1098/rspa.2010.0486
Publication status	Published - 8 Sept 2011

Keywords

p-Laplace Cauchy problem
p-Laplace evolution problem with stochastic forcing
q-sine basis
non-orthogonal spectral method
FINITE-ELEMENT APPROXIMATION
P-LAPLACIAN
FAST/SLOW DIFFUSION
GROWING SANDPILES
EQUATION
REGULARITY
LIMIT
MODEL

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title = "Approximation properties of the q-sine bases",

abstract = "For q >= 12/11, the eigenfunctions of the nonlinear eigenvalue problem associated with the one-dimensional q-Laplacian are known to form a Riesz basis of L-2(0, 1). We examine in this paper the approximation properties of this family of functions and its dual, and establish a non-orthogonal spectral method for the p-poisson boundary value problem and its corresponding parabolic time-evolution initial value problem with stochastic forcing. The principal objective of our analysis is the determination of optimal values of q for which the best approximation is achieved for a given p problem.",

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author = "Lyonell Boulton and Gabriel Lord",

year = "2011",

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doi = "10.1098/rspa.2010.0486",

language = "English",

volume = "467",

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journal = "Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences",

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TY - JOUR

T1 - Approximation properties of the q-sine bases

AU - Boulton, Lyonell

AU - Lord, Gabriel

PY - 2011/9/8

Y1 - 2011/9/8

N2 - For q >= 12/11, the eigenfunctions of the nonlinear eigenvalue problem associated with the one-dimensional q-Laplacian are known to form a Riesz basis of L-2(0, 1). We examine in this paper the approximation properties of this family of functions and its dual, and establish a non-orthogonal spectral method for the p-poisson boundary value problem and its corresponding parabolic time-evolution initial value problem with stochastic forcing. The principal objective of our analysis is the determination of optimal values of q for which the best approximation is achieved for a given p problem.

AB - For q >= 12/11, the eigenfunctions of the nonlinear eigenvalue problem associated with the one-dimensional q-Laplacian are known to form a Riesz basis of L-2(0, 1). We examine in this paper the approximation properties of this family of functions and its dual, and establish a non-orthogonal spectral method for the p-poisson boundary value problem and its corresponding parabolic time-evolution initial value problem with stochastic forcing. The principal objective of our analysis is the determination of optimal values of q for which the best approximation is achieved for a given p problem.

KW - p-Laplace Cauchy problem

KW - p-Laplace evolution problem with stochastic forcing

KW - q-sine basis

KW - non-orthogonal spectral method

KW - FINITE-ELEMENT APPROXIMATION

KW - P-LAPLACIAN

KW - FAST/SLOW DIFFUSION

KW - GROWING SANDPILES

KW - EQUATION

KW - REGULARITY

KW - LIMIT

KW - MODEL

U2 - 10.1098/rspa.2010.0486

DO - 10.1098/rspa.2010.0486

M3 - Article

SN - 1364-5021

VL - 467

SP - 2690

EP - 2711

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

IS - 2133

ER -

Approximation properties of the q-sine bases

Abstract

Keywords

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