Seven-point difference schemes for hyperbolic equations
نویسندگان
چکیده
منابع مشابه
Seven-Point Difference Schemes for Hyperbolic Equations
A necessary and sufficient condition is given for all hyperbolic difference schemes that use up to nine mesh points to be of second-order accuracy. We also construct a new difference scheme for two-dimensional hyperbolic systems of conservation laws. The scheme is of second-order accuracy and requires knowledge of only seven mesh points. A stability condition is obtained and is utilized in nume...
متن کاملOn Difference Schemes for Hyperbolic-Parabolic Equations
The nonlocal boundary value problem for a hyperbolic-parabolic equation in a Hilbert space H is considered. The difference schemes approximately solving this boundary value problem are presented. The stability estimates for the solution of these difference schemes are established. In applications, the stability estimates for the solutions of the difference schemes of the mixed type boundary val...
متن کاملNonstandard finite difference schemes for differential equations
In this paper, the reorganization of the denominator of the discrete derivative and nonlocal approximation of nonlinear terms are used in the design of nonstandard finite difference schemes (NSFDs). Numerical examples confirming then efficiency of schemes, for some differential equations are provided. In order to illustrate the accuracy of the new NSFDs, the numerical results are compared with ...
متن کاملOptimized Difference Schemes for Multidimensional Hyperbolic Partial Differential Equations
In numerical solutions to hyperbolic partial differential equations in multidimensions, in addition to dispersion and dissipation errors, there is a grid-related error (referred to as isotropy error or numerical anisotropy) that affects the directional dependence of the wave propagation. Difference schemes are mostly analyzed and optimized in one dimension, wherein the anisotropy correction may...
متن کاملOn Difference Schemes for Hyperbolic Equations with Discontinuous Initial Values
in the upper halfplane. It is well known that if fix) is a sufficiently smooth function (1.1) can be closely approximated by stable difference schemes, and very realistic error bounds are given in a number of papers (see, e.g., Lax [6]). But in applications there often arise initial functions, with simple discontinuities or discontinuities in the higher derivatives. A discontinuity in/(.-c) pro...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1975
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1975-0398114-1