Integrating linear ordinary fourth-order differential equations in the MAPLE programming environment

Authors

DOI:

https://doi.org/10.15587/1729-4061.2021.233944

Keywords:

computer simulation, ordinary fourth-order differential equations, generalized power series, regular special points

Abstract

This paper reports a method to solve ordinary fourth-order differential equations in the form of ordinary power series and, for the case of regular special points, in the form of generalized power series. An algorithm has been constructed and a program has been developed in the MAPLE environment (Waterloo, Ontario, Canada) in order to solve the fourth-order differential equations. All types of solutions depending on the roots of the governing equation have been considered. The examples of solutions to the fourth-order differential equations are given; they have been compared with the results available in the literature that demonstrate excellent agreement with the calculations reported here, which confirms the effectiveness of the developed programs. A special feature of this work is that the accuracy of the results is controlled by the number of terms in the power series and the number of symbols (up to 20) in decimal mantissa in numerical calculations. Therefore, almost any accuracy allowed for a given electronic computing machine or computer is achievable. The proposed symbolic-numerical method and the work program could be successfully used for solving eigenvalue problems, in which controlled accuracy is very important as the eigenfunctions are extremely (exponentially) sensitive to the accuracy of eigenvalues found. The developed algorithm could be implemented in other known computer algebra packages such as REDUCE (Santa Monica, CA), MATHEMATICA (USA), MAXIMA (USA), and others. The program for solving ordinary fourth-order differential equations could be used to construct Green’s functions of boundary problems, to solve differential equations with private derivatives, a system of Hamilton’s differential equations, and other problems related to mathematical physics.

Author Biographies

Irina Belyaeva, Belgorod State University

PhD, Associate Professor

Department of Computer Science, Natural Sciences and Teaching Methods

Igor Kirichenko, Kharkiv National Automobile and Highway University

Doctor of Physic-Mathematical Sciences, Professor

Department of Higher Mathematics

Oleh Ptashnyi, Kharkiv National Automobile and Highway University

PhD, Associate Professor

Department of Higher Mathematics

Natalia Chekanova, Kharkiv National Automobile and Highway University

PhD, Associate Professor

Department of Higher Mathematics

Tetiana Yarkho, Kharkiv National Automobile and Highway University

Doctor of Pedagogical Sciences, Professor

Department of Higher Mathematics

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Published

2021-06-29

How to Cite

Belyaeva, I., Kirichenko, I., Ptashnyi, O., Chekanova, N., & Yarkho, T. (2021). Integrating linear ordinary fourth-order differential equations in the MAPLE programming environment . Eastern-European Journal of Enterprise Technologies, 3(4 (111), 51–57. https://doi.org/10.15587/1729-4061.2021.233944

Issue

Vol. 3 No. 4 (111) (2021): Mathematics and Cybernetics - applied aspects

Section

Mathematics and Cybernetics - applied aspects

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Copyright (c) 2021 Irina Belyaeva, Natalia Chekanova, Igor Kirichenko, Oleh Ptashnyi, Tetiana Yarkho

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