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Stable Matching of Difference Schemes
SIAM Journal on Numerical Analysis, 1972Approximations that result from the natural matching of two stable dissipative difference schemes across a coordinate line are shown to be stable. The basic idea is to reformulate the matching scheme consistent to an equivalent initial boundary value problem and to verify the algebraic conditions for stability of such systems. An interesting comparison
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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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Multisplitting with Different Weighting Schemes
SIAM Journal on Matrix Analysis and Applications, 1989Parallel algorithms generated by multisplittings are considered. A parallel algorithm may be formed, first, by concurrently executing the iteration associated with each splitting, and second, by forming a weighted sum of these computations. However, it is not imperative that the weighting be done last.
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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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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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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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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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