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Thermodynamically matched difference schemes
USSR Computational Mathematics and Mathematical Physics, 1989Abstract A class of difference schemes which approximate the system of one-dimensional non-stationary equations of gas dynamics in Lagrange mass variables is considered. The homogeneous difference schemes satisfy the scheme matching principle and the equation of state of an ideal gas.
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Regularization of difference schemes
USSR Computational Mathematics and Mathematical Physics, 1967Abstract WE examine the possibilities of transforming or regularizing schemes in such a way that the new schemes are stable and satisfy auxiliary requirements as regards accuracy and economy. Difference schemes are treated as operator equations in real linear normed space [1, 2].
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Additive Operator-Difference Schemes
2013Applied mathematical modeling is concerned with solving unsteady problems. Splitting schemes are attributed to the transition from a complex problem to a chain of simpler problems. This book shows how to construct additive difference schemes (splitting schemes) to solve approximately unsteady multi-dimensional problems for PDEs.
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Three-Level Difference Schemes
2002Along with two-level difference schemes, three-level schemes are often also used to solve numerically non-stationary problems of mathematical physics. Such difference schemes are typical if we consider second-order evolution equations, one example of which is the equation of oscillations.
A. A. Samarskii +2 more
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2002
After having replaced a non-stationary problem of mathematical physics by its finite difference or finite element discretization in space, we obtain the Cauchy problem for a system of ordinary differential equations which is considered in a Hilbert grid space. The discretisation in time yields an operator-difference scheme.
A. A. Samarskii +2 more
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After having replaced a non-stationary problem of mathematical physics by its finite difference or finite element discretization in space, we obtain the Cauchy problem for a system of ordinary differential equations which is considered in a Hilbert grid space. The discretisation in time yields an operator-difference scheme.
A. A. Samarskii +2 more
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1994
Let us associate to the Cauchy problem (1.1) of Chapter 1 the corresponding difference problem $$ D_{uk} + A_{uk} = \varphi _k ,{\text{ }}1 \leqslant k \leqslant N,u_0 = u_o (\tau ). $$ (0.1) Here N is a fixed positive integer, τ = 1/N, Du k = (u k -uk-1)/τ; u τ = {u k } 1 N , φ τ = {φ k } 1 N are the unknown and the given grid functions with
A. Ashyralyev, P. E. Sobolevskii
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Let us associate to the Cauchy problem (1.1) of Chapter 1 the corresponding difference problem $$ D_{uk} + A_{uk} = \varphi _k ,{\text{ }}1 \leqslant k \leqslant N,u_0 = u_o (\tau ). $$ (0.1) Here N is a fixed positive integer, τ = 1/N, Du k = (u k -uk-1)/τ; u τ = {u k } 1 N , φ τ = {φ k } 1 N are the unknown and the given grid functions with
A. Ashyralyev, P. E. Sobolevskii
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1983
We consider a general system of conservation laws $$ {{u}_{t}}{\text{ + }}f{{(u)}_{x}} = 0,\quad x \in R,\;\quad t > 0, $$ (19.1) where u = (u 1,⋯,u n), with initial data $$ u(x,0) = {{u}_{0}}(x),\quad x \in R. $$ (19.2) The system (19.1) is assumed to be hyperbolic and genuinely nonlinear in each characteristic field, in some open ...
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We consider a general system of conservation laws $$ {{u}_{t}}{\text{ + }}f{{(u)}_{x}} = 0,\quad x \in R,\;\quad t > 0, $$ (19.1) where u = (u 1,⋯,u n), with initial data $$ u(x,0) = {{u}_{0}}(x),\quad x \in R. $$ (19.2) The system (19.1) is assumed to be hyperbolic and genuinely nonlinear in each characteristic field, in some open ...
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Continuity 3 - Difference Schemes
2010We have seen that it is possible to place upper bounds on the continuity of a scheme by carrying out eigenanalysis around a mark point. In principle these upper bounds can be tightened by doing this analysis for powers of the scheme, which give additional markpoints.
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Stability of Difference Schemes
2013The most powerful and most general method for constructing approximate solutions of hyperbolic partial differential equations with prescribed initial values is to discretize the space and time variables and solve the resulting finite system of equations. How to discretize is a subtle matter, as we shall demonstrate.
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Difference schemes on “oblique” nets
USSR Computational Mathematics and Mathematical Physics, 1965Samarskij, A. A., Gulin, A. V.
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