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Reminiscences about Difference Schemes
Journal of Computational Physics, 1999The article is the keynote address given by the author at the symposium ``Gudunov's method for gas dynamics: Current applications and future developments'' held at Michigan University in May 1997 in honour of S. K. Godunov. It is concerned with which is nowadays called ``Godunov's scheme'' and its later modifications.
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Memoirs of finite difference schemes
Journal of Computational PhysicszbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On a finite difference scheme for Burgers’ equation
Applied Mathematics and Computation, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kanti Pandey +2 more
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Similarities and differences in the kinetics of the michaelis scheme and the Henri scheme
Journal of Theoretical Biology, 1970Most steady state enzyme kinetics are consistent with the Henri scheme, (ES)E + S → E + Products, as well as with the common Michaelis scheme. The pre-steady-state time course of product can be used to distinguish between the schemes. Relaxation kinetic measurements do not offer a simple method for separating the reversible Michaelis scheme from the ...
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$\epsilon$-convergent splines difference scheme
Publicationes Mathematicae Debrecen, 1994A singular boundary value problem \(- \varepsilon u'' + p(x)u = f(x)\), \(x \in [0,1]\), \(u(0) = u_ 0\), \(u(1) = u_ 1\) is solved where \(0 < \varepsilon \ll 1\), \(p,f \in C^ 2 [0,1]\), \(p(x) \geq \beta > 0\) and \(p'(0) = p'(1) = 0\). A method is given for which the truncation error \(R\) is bounded by \(\| R \| < Mh \sqrt \varepsilon\) in the ...
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1984
To arrive at finite difference equations modeling magnetohydrodynamic equilibrium we use a technique that is motivated by the finite element method [3]. First we develop a second order accurate numerical quadrature formula for the Hamiltonian E based on a rectangular grid of mesh points over a unit cube of the space with coordinates s, u and v.
Frances Bauer +2 more
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To arrive at finite difference equations modeling magnetohydrodynamic equilibrium we use a technique that is motivated by the finite element method [3]. First we develop a second order accurate numerical quadrature formula for the Hamiltonian E based on a rectangular grid of mesh points over a unit cube of the space with coordinates s, u and v.
Frances Bauer +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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1994
Let us consider the problem of approximating the function e-z near z = 0 by rational functions $$ \begin{gathered} R_{j,l} (z) = \frac{{P_{j,l} (z)}} {{Q_{j,l} (z)}} = \frac{{a_0 + a_1 z + ... + a_j z^j }} {{}}, \hfill \\ a_r = a_r (j,l),r = 1...j,b_r = b_r (j,l),r = 1...,l,a_j \ne 0,b_l \ne 0,b_0 \ne 0. \hfill \\ \end{gathered} $$
A. Ashyralyev, P. E. Sobolevskii
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Let us consider the problem of approximating the function e-z near z = 0 by rational functions $$ \begin{gathered} R_{j,l} (z) = \frac{{P_{j,l} (z)}} {{Q_{j,l} (z)}} = \frac{{a_0 + a_1 z + ... + a_j z^j }} {{}}, \hfill \\ a_r = a_r (j,l),r = 1...j,b_r = b_r (j,l),r = 1...,l,a_j \ne 0,b_l \ne 0,b_0 \ne 0. \hfill \\ \end{gathered} $$
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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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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