title: Ð Ð°Ð·ÑÐ°Ð±Ð¾ÑÐºÐ° Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½ÑÑ ÑÑÐµÐ´ÑÑÐ² Ð´Ð»Ñ Ð²Ð¸Ð·ÑÐ°Ð»ÑÐ½Ð¾Ð¹ Ð¾ÑÐµÐ½ÐºÐ¸ ÐºÐ°ÑÐµÑÑÐ²Ð° ÑÐ¸ÑÐ»ÐµÐ½Ð½ÑÑ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² Ð¸Ð½ÑÐµÐ³ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Development of software tools for visual assessment of the quality of numerical integration methods
Creators: name: Ð¨ÐµÐ»ÑÐ³Ð¾Ð², Ð¡ÐµÑÐ³ÐµÐ¹
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2022
Subjects: Ð¼Ð¾Ð´ÐµÐ»Ñ ÐÐ¾ÑÐºÐ¸-ÐÐ¾Ð»ÑÑÐµÑÑÑ
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ÑÐ¾Ñ ÑÐ°Ð½ÐµÐ½Ð¸Ðµ ÑÑÑÑÐºÑÑÑ Ð´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½ÑÑ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹
Lotka-Volterra model
mathematical pendulum
Euler method
Runge-Kutta method
phase portrait
numerical flow
preservation of structures of differential equations

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description: The topic of the final qualifying work: "Development of software tools for visual assessment of the quality of numerical integration methods". The purpose of this work is to study the preservation of the structures of differential equations by the example of the Lotka-Volterra model and the pendulum when integrated by various methods, such as:- explicit Euler method;- Euler's symplectic method;- the Runge-Kutta method. Tasks that were solved during the study: 1. Construction of Lotka-Volterra and pendulum models. 2. Application of integration methods to models. 3. Visualization of solutions of differential equations. 4. Analysis of the obtained solutions for the preservation of structures and comparison between them. 5. Software implementation of methodsThe work was carried out using Python. With its help, programs were implemented to visualize solutions of differential equations of the integration methods under consideration. As a result, graphs of solutions of differential equations were constructed. They were analyzed to preserve the structures of differential equations. Numerical flows of these systems were also constructed and an analysis was carried out to preserve the area of these flows.