In this paper, based on the idea of El-Mistikawy and Werle[1] we construct a difference scheme for a singularly perturbed self-adjoint ordinary differential equation in conservation form. We prove that it is a uniform...In this paper, based on the idea of El-Mistikawy and Werle[1] we construct a difference scheme for a singularly perturbed self-adjoint ordinary differential equation in conservation form. We prove that it is a uniformly convergent second order scheme.展开更多
Abstract Let $\Omega \subset R^m (m\ge 1)$ be a bounded domain with piecewise smooth boundary $\partial \Omega$. Let t and r be positive integers with t > r + 1. We consider the eigenvalue problems (1.1) and (1.2),...Abstract Let $\Omega \subset R^m (m\ge 1)$ be a bounded domain with piecewise smooth boundary $\partial \Omega$. Let t and r be positive integers with t > r + 1. We consider the eigenvalue problems (1.1) and (1.2), and obtain Theorem 1 and Theorem 2, which generalize the results in [1,2,5].展开更多
Let Ωbelong to R^m （m≥ 2） be a bounded domain with piecewise smooth and Lipschitz boundary δΩ Let t and r be two nonnegative integers with t ≥ r ＋ 1. In this paper, we consider the variable-coefficient eigenva...Let Ωbelong to R^m （m≥ 2） be a bounded domain with piecewise smooth and Lipschitz boundary δΩ Let t and r be two nonnegative integers with t ≥ r ＋ 1. In this paper, we consider the variable-coefficient eigenvalue problems with uniformly elliptic differential operators on the left-hand side and （-Δ）^T on the right-hand side. Some upper bounds of the arbitrary eigenvalue are obtained, and several known results are generalized.展开更多
Based on the work of Shu [SIAM J. Sci. Stat. Comput, 9 （1988）, pp.1073-1084], we construct a class of high order multi-step temporal discretization procedure for finite volume Hermite weighted essential non-oscillat...Based on the work of Shu [SIAM J. Sci. Stat. Comput, 9 （1988）, pp.1073-1084], we construct a class of high order multi-step temporal discretization procedure for finite volume Hermite weighted essential non-oscillatory （HWENO） methods to solve hyperbolic conservation laws. The key feature of the multi-step temporal discretization procedure is to use variable time step with strong stability preserving （SSP）. The multi-step tem- poral discretization methods can make full use of computed information with HWENO spatial discretization by holding the former computational values. Extensive numerical experiments are presented to demonstrate that the finite volume HWENO schemes with multi-step diseretization can achieve high order accuracy and maintain non-oscillatory properties near discontinuous region of the solution.展开更多
文摘In this paper, based on the idea of El-Mistikawy and Werle[1] we construct a difference scheme for a singularly perturbed self-adjoint ordinary differential equation in conservation form. We prove that it is a uniformly convergent second order scheme.
文摘Abstract Let $\Omega \subset R^m (m\ge 1)$ be a bounded domain with piecewise smooth boundary $\partial \Omega$. Let t and r be positive integers with t > r + 1. We consider the eigenvalue problems (1.1) and (1.2), and obtain Theorem 1 and Theorem 2, which generalize the results in [1,2,5].
基金Supported by the National Natural Science Foundation of China(No.10471063)
文摘Let Ωbelong to R^m （m≥ 2） be a bounded domain with piecewise smooth and Lipschitz boundary δΩ Let t and r be two nonnegative integers with t ≥ r ＋ 1. In this paper, we consider the variable-coefficient eigenvalue problems with uniformly elliptic differential operators on the left-hand side and （-Δ）^T on the right-hand side. Some upper bounds of the arbitrary eigenvalue are obtained, and several known results are generalized.
文摘Based on the work of Shu [SIAM J. Sci. Stat. Comput, 9 （1988）, pp.1073-1084], we construct a class of high order multi-step temporal discretization procedure for finite volume Hermite weighted essential non-oscillatory （HWENO） methods to solve hyperbolic conservation laws. The key feature of the multi-step temporal discretization procedure is to use variable time step with strong stability preserving （SSP）. The multi-step tem- poral discretization methods can make full use of computed information with HWENO spatial discretization by holding the former computational values. Extensive numerical experiments are presented to demonstrate that the finite volume HWENO schemes with multi-step diseretization can achieve high order accuracy and maintain non-oscillatory properties near discontinuous region of the solution.
