Year: 1988
Author: He-Ping Ma, Ben-Yu Guo
Journal of Computational Mathematics, Vol. 6 (1988), Iss. 1 : pp. 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 Burgers-like equations. $$\begin{cases} ∂_iu+F(u)_x-vu_{zx}=0, & -1≤x≤1, 0＜t≤T \\ u (-1,t) =u (1,t) =0, & 0≤t≤T & (0.1) \\ u (x,0) =u_0(x), & -1≤x≤1 \end{cases}$$ 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 generalized stability and convergence.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1988-JCM-9497
Journal of Computational Mathematics, Vol. 6 (1988), Iss. 1 : pp. 48–53
Published online: 1988-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 6