SYMBOLIC-NUMERIC APPROACH FOR SOLVING LINEAR DIFFERENTIAL EQUATIONS OF THE FOURTH ORDER
AbstractThis paper presents a symbolic-numeric approach for solving linear differential equations of the fourth order in the form of generalized power series. The working program allows to find solutions to differential equations of the fourth order in the form of power series, generally, of any order, but is limited by capabilities of a given computer. Some examples of solving differential equations of the fourth order are presented, which show the efficiency of the developed program. The results are consistent with the available literature data.
Bahvalov, N.S., Dhidkov, N.P., Kobelkov, G.M., 2011. Numerical methods (Chislennyemetody). Binom. Laboratory of knowledge. Moscow, p 640. (in Russian).
Kontorovich, L.V., V.I. Krylov, 1962. Approximate methods of higher analysis. FIZMATGIZ, Moscow, 1962, 5th ed; Engtransl of 3rded, Interscience, New York and Noordhoff, Groniongen 1958.
Collatz, L.: EigenwertaufgabenmittechnischenAnwendungen. Leipzig: AkademischeVerlagsgesellschaftGeest u. Portig K.-G. 1949. 466 S.
FÃ¶ppl, August. Drang und zwang. Vol. 2. R. Oldenbourg, 1928.
Forst, W., Hoffmann, D., 2012. Explore function theory with Maple (Funktionentheorieerkundenmit Maple). Springer-Verlag Berlin Heidelbergâ€.
Easayan, A.P., Chybarikov, V.N., Dobrovolskii, N.M., Martynyuk, Yu.M., 2007. Control structures and data structures in Maple. Tula: Izd-vogos.ped. yn-ta im. L.N. Tolstogo. (in Russian)
Franco Vivaldi, 2018. Experimental Mathematics with Maple. Rome: CRC Press.
Kamke, E., 1965. Manual of ordinary differential equations. Moscow: Nauka. (In Russian)
Ince, E.L., 1939. Differential equations. London: University Press.
Sansone, J., 1948. Ordinary differential equations. V.1. Rome: CRC Press.
Knesckke, A. (1961), F. G. Tricomi, Differential Equations. X + 273 S. London 1961. Blackie & Son Ltd. Preisgeb. 50 s. Z. angew. Math. Mech., 41: 470-470.( Accessed from https://onlinelibrary.wiley.com/doi/abs/10.1002/zamm.19610411027)
Belyaeva, I.N., Chekanov, N.A., Chekanova, N.N., 2016. Program of symbol-numeric integration of linear differential equation of four order. Patent of RU, Program for ECM, â„–2016611952. (in Russian)
The submitter hereby warrants that the Work (collectively, the “Materials”) is original and that he/she is the author of the Materials. To the extent the Materials incorporate text passages, figures, data or other material from the works of others, the undersigned has obtained any necessary permissions. Where necessary, the undersigned has obtained all third party permissions and consents to grant the license above and has all copies of such permissions and consents.
The submitter represents that he/she has the power and authority to make and execute this assignment. The submitter agrees to indemnify and hold harmless the COMPUSOFT from any damage or expense that may arise in the event of a breach of any of the warranties set forth above. For authenticity, validity and originality of the research paper the author/authors will be totally responsible.