×
Dorodnitsyn, V. A.

Transformation groups in network spaces. (English. Russian original) Zbl 0727.65074

J. Sov. Math. 55, No. 1, 1490-1517 (1991); translation from Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Noveishie Dostizh. 34, 149-191 (1989).
See the review in Zbl 0716.65085.

Cited in 1 Review
Cited in 31 Documents

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65N06 Finite difference methods for boundary value problems involving PDEs

Keywords:

groups of transformations; Lie-Bäcklund groups; invariance of difference equations; formal Newton series; ideal; Lie-Bäcklund operators; uniform network; Noether identity

Citations:

Zbl 0716.65085
Cite Review PDF
Full Text: DOI

References:

[1] A. O. Gel’fond, Calculus of Finite Differences [in Russian], Fizmatgiz, Moscow (1967).
[2] V. A. Dorodnitsyn, ?Taylor group and transformations preserving difference derivatives,? Preprint Inst. Prikl. Mat. (IPM) AN SSSR, Moscow (1987), No. 67.
[3] V. A. Dorodnitsyn, ?Newton group and commutation properties of Lie-Bäcklund operators in net spaces,? Preprint, Inst. Prikl. Mat. (IPM) AN SSSR, Moscow (1988), No. 175.
[4] N. Kh. Ibragimov, Transformation Groups in Mathematical Physics [in Russian], Nauka, Moscow (1983).
[5] A. A. Markov, Calculus of Finite Differences [in Russian], Odessa (1910).
[6] L. V. Ovsyannikov, ?Group properties of the equation of nonlinear thermal conductivity,? Dokl. Akad. Nauk SSSR,125, No. 3, 492?495 (1959). · Zbl 0092.09903
[7] L. V. Ovsyannikov, Group Analysis of Differential Equations [in Russian], Nauka, Moscow (1978). · Zbl 0484.58001
[8] A. A. Samarskii, Theory of Difference Schemes [in Russian], Nauka, Moscow (1977). · Zbl 0368.65031
[9] A. A. Samarskii and I. M. Sobol’, ?Examples of numerical calculation of temperature fields,? Zh. Vychisl. Mat. Mat. Fiz.,3, No. 4, 702?719 (1963).
[10] N. G. Chebotarev, Theory of Lie Groups [in Russian], GITTL, Leningrad (1940).
[11] Yu. I. Shokin, Numerical Methods of Gas Dynamics. Invariant Difference Schemes [in Russian], Novosibirsk State Univ. (1977).
[12] R. I. Yamilov, ?Conservation laws for the Korteweg-de Vries difference equation,? Dinamika Neodnorodnoi Zhidkosti,44, 164?173 (1980). · Zbl 0516.35070
[13] N. N. Yanenko and Yu. I. Shokin, ?Group classification of difference schemes for the system of equations of gas dynamics,? Tr. Mat. Inst. Akad. Nauk SSSR,122, 85?96 (1973).
[14] J. L. Lagrange, ?Memoire sur la methode d’interpolation,? Oeuvres V (1783), pp. 663?684.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.