Geodesic
From differential equations to difference equations
Matematičeskoe obrazovanie, no. 3 (2023), pp. 38-47 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The most popular, widely used method in regards to solving first order linear equations is through induction. However there are similar techniques that can be employed to obtain a general solution without the use of mathematical induction. Also, general solutions can be provided by borrowing a method based on the characteristic equation for second order linear difference equations of the Euler-Cauchy type. These differential equations are an important aspect of learning as they provide a fundamental foundation of tools and intuition that lead to partial differential equations which are used to describe phenomena in natural sciences. 
@article{MO_2023_3_a6,
     author = {U. Goginava and F. M. Mukhamedov},
     title = {From differential equations to difference equations},
     journal = {Matemati\v{c}eskoe obrazovanie},
     pages = {38--47},
     year = {2023},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MO_2023_3_a6/}
}
TY  - JOUR
AU  - U. Goginava
AU  - F. M. Mukhamedov
TI  - From differential equations to difference equations
JO  - Matematičeskoe obrazovanie
PY  - 2023
SP  - 38
EP  - 47
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/MO_2023_3_a6/
LA  - ru
ID  - MO_2023_3_a6
ER  - 
%0 Journal Article
%A U. Goginava
%A F. M. Mukhamedov
%T From differential equations to difference equations
%J Matematičeskoe obrazovanie
%D 2023
%P 38-47
%N 3
%U http://geodesic.mathdoc.fr/item/MO_2023_3_a6/
%G ru
%F MO_2023_3_a6
U. Goginava; F. M. Mukhamedov. From differential equations to difference equations. Matematičeskoe obrazovanie, no. 3 (2023), pp. 38-47. http://geodesic.mathdoc.fr/item/MO_2023_3_a6/

[1] C. R. Adams, “On the irregular cases of linear ordinary difference equations”, Trans. Amer. Math. Soc., 30 (1928), 507–541 | DOI | MR

[2] G. D. Birkhoff, “Formal theory of irregular linear drfference equations”, Acta Math., 54 (1930), 205–246 | DOI | MR

[3] S. Elaydi, An Introduction to Difference Equations, Springer Science+Business Media, Inc., 2005 | MR | Zbl

[4] S. Goldberg, An Inroduction to Difference Equations, Wiley, New York, 1958 | MR

[5] A. Hongyo, N. Yamaoka, “General solution of second-order linear difference equations of Euler type”, Opuscula Math., 37 (2012), 389–402 | DOI | MR

[6] G. Strang, “Sums and differences vs. integrals and derivatives”, College Math. J., 21 (1990), 20–27 | DOI

[7] R. Wong, H. Li, “Asymptotic expansions for second-order linear difference equations”, J. Comput. Appl. Math., 41 (1992), 65–94 | DOI | MR | Zbl

[8] A. Zygmund, Trigonemetric Series, Cambridge Univ. Press, 2002 | MR