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Article

Chrastinová, Veronika ; Tryhuk, Václav
Parallelisms between differential and difference equations. (English). Mathematica Bohemica, vol. 137 (2012), issue 2, pp. 175-185
MSC: 34A34, 34C14, 39A05, 39A12 | MR 2978263 | Zbl 1265.34002 | DOI: 10.21136/MB.2012.142863
Keywords:
ordinary differential equation; ordinary difference equation; first integral; symmetry; infinitesimal symmetry; moving frame
Summary:
The paper deals with the higher-order ordinary differential equations and the analogous higher-order difference equations and compares the corresponding fundamental concepts. Important dissimilarities appear for the moving frame method.
References:
[1] Hydon, P. E.: Symmetries and first integrals of ordinary difference equations. Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 456 2835-2855 (2000). DOI 10.1098/rspa.2000.0643 | MR 1843844 | Zbl 0991.39005
[2] Olver, P. J.: Applications of Lie Groups to Differential Equations. 2nd Graduate Texts in Mathematics, 107, Springer, New York (1993). MR 1240056 | Zbl 0785.58003
[3] Olver, P. J.: Equivalence, Invariants, and Symmetry. Cambridge University Press, Cambridge (1995). MR 1337276 | Zbl 0837.58001
[4] Tryhuk, V., Chrastinová, V.: Equivalence of difference equations within the web theory. Mathematica Slovaca, to appear.
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