Volume 6, Issue 1
The Chebyshev Spectral Method for Burgers-Like Equations
DOI:

J. Comp. Math., 6 (1988), pp. 48-53

Published online: 1988-06

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• Abstract

The Chebyshev polynomials have good approximation properties which are not affected by boundary values. They have higher resolution near the boundary than in the interior and are suitable for problems in which the solution changes rapidly near the boundary. Also, they can be calculated by FFT. Thus they are used mostly for initial-boundary value problems for P.D.E.'s(see [1,3-4,6,8-11]).Maday and Quarterom discussed the convergence of Legendre and Chebyshev spectral approximations to the steady Burgers equation. In this paper we consider Bur gers-like equations. where $F\in C(R)$ and there exists a positive function $A\in C(R)$ and a constant p›1 such that $|F(z+y)-F(z)|\leq A(z)(|y|+|y|^p)$. We develop a Chebyshev spectral scheme and a pseudospectral scheme for solving(0.1) and establish their generlized.

• Keywords

@Article{JCM-6-48, author = {}, title = {The Chebyshev Spectral Method for Burgers-Like Equations}, journal = {Journal of Computational Mathematics}, year = {1988}, volume = {6}, number = {1}, pages = {48--53}, abstract = { The Chebyshev polynomials have good approximation properties which are not affected by boundary values. They have higher resolution near the boundary than in the interior and are suitable for problems in which the solution changes rapidly near the boundary. Also, they can be calculated by FFT. Thus they are used mostly for initial-boundary value problems for P.D.E.'s(see [1,3-4,6,8-11]).Maday and Quarterom discussed the convergence of Legendre and Chebyshev spectral approximations to the steady Burgers equation. In this paper we consider Bur gers-like equations. where $F\in C(R)$ and there exists a positive function $A\in C(R)$ and a constant p›1 such that $|F(z+y)-F(z)|\leq A(z)(|y|+|y|^p)$. We develop a Chebyshev spectral scheme and a pseudospectral scheme for solving(0.1) and establish their generlized. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9497.html} }
TY - JOUR T1 - The Chebyshev Spectral Method for Burgers-Like Equations JO - Journal of Computational Mathematics VL - 1 SP - 48 EP - 53 PY - 1988 DA - 1988/06 SN - 6 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9497.html KW - AB - The Chebyshev polynomials have good approximation properties which are not affected by boundary values. They have higher resolution near the boundary than in the interior and are suitable for problems in which the solution changes rapidly near the boundary. Also, they can be calculated by FFT. Thus they are used mostly for initial-boundary value problems for P.D.E.'s(see [1,3-4,6,8-11]).Maday and Quarterom discussed the convergence of Legendre and Chebyshev spectral approximations to the steady Burgers equation. In this paper we consider Bur gers-like equations. where $F\in C(R)$ and there exists a positive function $A\in C(R)$ and a constant p›1 such that $|F(z+y)-F(z)|\leq A(z)(|y|+|y|^p)$. We develop a Chebyshev spectral scheme and a pseudospectral scheme for solving(0.1) and establish their generlized.