Approximations by orthonormal mapped Chebyshev functions for higher-dimensional problems in unbounded domains

DOI10.1016/j.cam.2013.09.024zbMath1293.65161OpenAlexW2171629345MaRDI QIDQ2511290

Li-Lian Wang, Jie Shen, Hai-jun Yu

Publication date: 5 August 2014

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2013.09.024

zbMATH Keywords

error estimatesunbounded domainsspectral methodhyperbolic crosshigher-dimensional problemsmapped Chebyshev functions

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Error bounds for boundary value problems involving PDEs (65N15)

Related Items (12)

An efficient spectral-Galerkin method for fractional reaction-diffusion equations in unbounded domains ⋮ Chebyshev rational spectral method for long-short wave equations ⋮ Least squares support vector regression for differential equations on unbounded domains ⋮ A Fast Petrov--Galerkin Spectral Method for the Multidimensional Boltzmann Equation Using Mapped Chebyshev Functions ⋮ Two efficient spectral methods for the nonlinear fractional wave equation in unbounded domain ⋮ A new collocation method using near-minimal Chebyshev quadrature nodes on a square ⋮ О двух асимптотических формулах в теории гиперболической дзета-функции решёток ⋮ A Petrov-Galerkin spectral method for the inelastic Boltzmann equation using mapped Chebyshev functions ⋮ Fast Fourier-like Mapped Chebyshev Spectral-Galerkin Methods for PDEs with Integral Fractional Laplacian in Unbounded Domains ⋮ Better Approximations of High Dimensional Smooth Functions by Deep Neural Networks with Rectified Power Units ⋮ Efficient Spectral-Element Methods for the Electronic Schrödinger Equation ⋮ Rational Spectral Methods for PDEs Involving Fractional Laplacian in Unbounded Domains

Cites Work

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• The optimization of convergence for Chebyshev polynomial methods in an unbounded domain
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• Efficient Spectral Sparse Grid Methods and Applications to High-Dimensional Elliptic Equations II. Unbounded Domains
• Spectral Methods
• Chebyshev rational spectral and pseudospectral methods on a semi‐infinite interval
• Efficient Spectral Sparse Grid Methods and Applications to High-Dimensional Elliptic Problems
• Sparse Spectral Approximations of High-Dimensional Problems Based on Hyperbolic Cross
• Sparse grids for the Schrödinger equation

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