VISUALIZATION OF NUMERICAL SOLUTIONS OF MATHEMATICAL PHYSICS EQUATIONS USING MAPLE
DOI:
https://doi.org/10.34132/mspc2025.01.14.05Keywords:
partial differential equations, numerical methods, grid method, equations of mathe-matical physics, Maple.Abstract
The theses consider the visualization of solutions to some mathematical physics problems obtained by numerical methods using the Maple mathematical package, such as: a mixed boundary value problem for the string oscillation equation, the heat conduction equation, and the Dirichlet problem for the Laplace equation. Although mixed boundary value problems have certain difficulties, there is a powerful arsenal of numerical methods and software tools that allow them to be solved. Using Maple for numerical solution of mathematical physics problems allows computer science students and engineers to concentrate on the essence of the problem, they do not have to waste time on complex implementation of numerical algorithms. The study of numerical methods involves their software implementation, which contributes to the development of programming skills, especially in the field of working with data sets, developing effective algorithms and optimizing code. Specialists with a deep understanding of numerical methods are in demand in many industries, including IT companies, which is why when studying such methods we combine the use of the mathematical package Maple and software implementation in various programming languages.
References
Nikitenko O.M. (2014). Maple: Solving engineering and scientific problems: a training manual. Kharkiv: NURE, 289 p. [in Ukrainian].
Vorobyova A.I., Kuriksha O.V. (2009) Symmetric analysis of partial differential equations using the Maple mathematical package. Scientific works of the Petro Mohyla Black Sea State University. Ser.: Computer Technologies, 106, vol. 93, pp. 75-79. [in Ukrainian].
Andrunyk V.A., Vysotska V.A., Pasichnyk V.V., Chyrun L.B., Chyrun L.V. (2020). Numerical Methods in Computer Science: Textbook - Lviv: Vydavnytstvo «Novyy svit – 2000», 470 p. [in Ukrainian].
Goy T.P., Kopach M.I., Fedak I.V. (2010) Approximate methods for solving differential equations. A textbook for students of the “mathematics” and “applied mathematics” training areas. – Ivano-Frankivsk: Publishing and design department of the Center for Information Technologies of Vasyl Stefanyk Precarpathian National University, 148 p. [in Ukrainian].
BrahinetsО., & Vorobyova А. (2022). Using the mathematical program Maple to solve systems of linear algebraic equations by direct numerical methods. Computer-integrated technologies: education, science, production, (47), 55-63. https://doi.org/10.36910/6775-2524-0560-2022-47-08 [in Ukrainian].
