Browsing by Author "Tadmor, Eitan"
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Item Analysis of the spectral vanishing method for periodic conservation laws(Copyright: Society for Industrial and Applied Mathematics, 1989-08) Maday, Yvon; Tadmor, EitanItem The CFL condition for spectral approximations to hyperbolic initial-boundary value problems.(American Mathematical Society, 1991-04) Gottlieb, David; Tadmor, EitanItem Convenient stability criteria for difference approximations of hyperbolic initial-boundary value problems(American Mathematical Society, 1985-04) Goldberg, Moshe; Tadmor, EitanItem Convenient stability criteria for difference approximations of hyperbolic initial-boundary value problems. II(American Mathematical Society, 1987-04) Goldberg, Moshe; Tadmor, EitanItem Convenient total variation diminishing conditions for nonlinear difference schemes(Copyright: Society for Industrial and Applied Mathematics, 1988-10) Tadmor, EitanItem Convergence of spectral methods for hyperbolic initial-boundary value systems(Copyright: Society for Industrial and Applied Mathematics, 1987-06) Gottlieb, David; Lustman, Liviu; Tadmor, EitanItem Convergence of spectral methods for hyperbolic initial-boundary value systems(Copyright: Society for Industrial and Applied Mathematics, 1987-06) Gottlieb, David; Lustman, Liviu; Tadmor, EitanItem Convergence of spectral methods for nonlinear conservation laws(Copyright: Society for Industrial and Applied Mathematics, 1989-02) 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 The convergence rate of Godunov type schemes(Copyright: Society for Industrial and Applied Mathematics, 1994-02) Nessyahu, Haim; Tadmor, Eitan; Tassa, TamirItem High order time discretization methods with the strong stability property(Copyright: Society for Industrial and Applied Mathematics, 2001) Gottlieb, Sigal; Shu, Chi-Wang; Tadmor, EitanIn this paper we review and further develop a class of strong stability-preserving (SSP) high-order time discretizations for semidiscrete method of lines approximations of partial differential equations.Previously termed TVD (total variation diminishing) time discretizations, these high-order time discretization methods preserve the strong stability properties of first-order Euler time stepping and have proved very useful, especially in solving hyperbolic partial differential equations.The new developments in this paper include the construction of optimal explicit SSP linear Runge–Kutta methods, their application to the strong stability of coercive approximations, a systematic study of explicit SSP multistep methods for nonlinear problems, and the study of the SSP property of implicit Runge–Kutta and multistep methods.Item The large-time behavior of the scalar, genuinely nonlinear Lax-Friedrichs scheme(American Mathematical Society, 1984-10) Tadmor, EitanItem 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 Local error estimates for discontinuous solutions of nonlinear hyperbolic equations(Copyright: Society for Industrial and Applied Mathematics, 1991-08) Tadmor, EitanItem Non-oscillatory central schemes for one- and two-dimensional MHD equations. II: high-order semi-discrete schemes.(Copyright: Society for Industrial and Applied Mathematics, 2006) Balbas, Jorge; Tadmor, EitanWe present a new family of high-resolution, nonoscillatory semidiscrete central schemes for the approximate solution of the ideal magnetohydrodynamics (MHD) equations. This is the second part of our work, where we are passing from the fully discrete staggered schemes in [J. Balb´as, E. Tadmor, and C.-C. Wu, J. Comput. Phys., 201 (2004), pp. 261–285] to the semidiscrete formulation advocated in [A. Kurganov and E. Tadmor, J. Comput. Phys., 160 (2000), pp. 241–282]. This semidiscrete formulation retains the simplicity of fully discrete central schemes while enhancing efficiency and adding versatility. The semidiscrete algorithm offers a wider range of options to implement its two key steps: nonoscillatory reconstruction of point values followed by the evolution of the corresponding point valued fluxes. We present the solution of several prototype MHD problems. Solutions of one-dimensional Brio–Wu shock-tube problems and the two-dimensional Kelvin–Helmholtz instability, Orszag–Tang vortex system, and the disruption of a high density cloud by a strong shock are carried out using third- and fourth-order central schemes based on the central WENO reconstructions. These results complement those presented in our earlier work and confirm the remarkable versatility and simplicity of central schemes as black-box, Jacobian-free MHD solvers. Furthermore, our numerical experiments demonstrate that this family of semidiscrete central schemes preserves the ∇ · B = 0-constraint within machine round-off error; happily, no constrained-transport enforcement is needed.Item Numerical viscosity and the entropy condition for conservative difference schemes(American Mathamatical Society, 1984-10) Tadmor, EitanItem The numerical viscosity of entropy stable schemes for systems of conservation laws. I.(American Mathematical Society, 1987-07) 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 On the convergence of difference approximations to scalar conservation laws.(American Mathematical Society, 1988-01) Osher, Stanley; Tadmor, EitanItem Scheme-independent stability criteria for difference approximations of hyperbolic initial-boundary value problems.(American Mathematical Society, 1978-10) Goldberg, Moshe; Tadmor, Eitan