Mathematics
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Item SPECTRAL METHODS FOR HYPERBOLIC PROBLEMS(1994-01) Tadmor, EitanWe review several topics concerning spectral approximations of time-dependent problems, primarily | the accuracy and stability of Fourier and Chebyshev methods for the approximate solutions of hyperbolic systems. To make these notes self contained, we begin with a very brief overview of Cauchy problems. Thus, the main focus of the first part is on hyperbolic systems which are dealt with two (related) tools: the energy method and Fourier analysis. The second part deals with spectral approximations. Here we introduce the main ingredients of spectral accuracy, Fourier and Chebyshev interpolants, aliasing, differentiation matrices ... The third part is devoted to Fourier method for the approximate solution of periodic systems. The questions of stability and convergence are answered by combining ideas from the first two sections. In this context we highlight the role of aliasing and smoothing; in particular, we explain how the lack of resolution might excite small scales weak instability, which is avoided by high modes smoothing. The forth and final part deals with non-periodic problems. We study the stability of the Chebyshev method, paying special attention to the intricate issue of the CFL stability restriction on the permitted time-step.Item The convergence rate of Godunov type schemes(Copyright: Society for Industrial and Applied Mathematics, 1994-02) Nessyahu, Haim; Tadmor, Eitan; Tassa, TamirItem Legendre pseudospectral viscosity method for nonlinear conservation laws(Copyright: Society for Industrial and Applied Mathematics, 1993-04) Maday, Yvon; Kaber, Sidi M. Ould; Tadmor, EitanItem The convergence rate of approximate solutions for nonlinear scalar conservation laws(Copyright: Society for Industrial and Applied Mathematics, 1992-12) Nessyahu, Haim; Tadmor, EitanItem Local error estimates for discontinuous solutions of nonlinear hyperbolic equations(Copyright: Society for Industrial and Applied Mathematics, 1991-08) Tadmor, EitanItem An O(N2) method for computing the eigensystem of N x N symmetric tri-diagonal matrices by the divide and conquer approach(Copyright: Society for Industrial and Applied Mathematics, 1990-01) Gill, Doron; Tadmor, EitanItem Analysis of the spectral vanishing method for periodic conservation laws(Copyright: Society for Industrial and Applied Mathematics, 1989-08) Maday, Yvon; Tadmor, EitanItem Convergence of spectral methods for nonlinear conservation laws(Copyright: Society for Industrial and Applied Mathematics, 1989-02) Tadmor, EitanItem Convenient total variation diminishing conditions for nonlinear difference schemes(Copyright: Society for Industrial and Applied Mathematics, 1988-10) Tadmor, EitanItem Stability analysis of finite-difference, pseudospectral and Fourier-Galerkin approximations for time-dependent problems(Copyright: Society for Industrial and Applied Mathematics, 1987-12) Tadmor, Eitan
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