title: Ð¡ÑÐ°Ð²Ð½Ð¸ÑÐµÐ»ÑÐ½ÑÐ¹ Ð°Ð½Ð°Ð»Ð¸Ð· Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð¾Ð² ÑÐµÑÐµÐ½Ð¸Ñ Ð¾Ð´Ð½Ð¾Ð¼ÐµÑÐ½ÑÑ Ð·Ð°Ð´Ð°Ñ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ ÑÐ¸Ð·Ð¸ÐºÐ¸ Ñ Ð°Ð´Ð°Ð¿ÑÐ°ÑÐ¸ÐµÐ¹ ÑÐµÑÐ¾Ðº
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: Comparative analysis of algorithms for solving one dimensional problems of mathematical physics with the adaptation of mesh
Creators: name: ÐÑÑÑÐ¾Ð¼ÑÑÐ¾Ð², ÐÐ²Ð³ÐµÐ½Ð¸Ð¹
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: 2021
Subjects: ÑÐ¸ÑÐ»ÐµÐ½Ð½ÑÐµ Ð¼ÐµÑÐ¾Ð´Ñ
Ð¼ÐµÑÐ¾Ð´ ÐºÐ¾Ð½ÐµÑÐ½ÑÑ ÑÐ°Ð·Ð½Ð¾ÑÑÐµÐ¹
Ð¼ÐµÑÐ¾Ð´ ÐºÐ¾Ð½ÐµÑÐ½ÑÑ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ¾Ð²
Ð°Ð´Ð°Ð¿ÑÐ°ÑÐ¸Ñ ÑÐµÑÐ¾Ðº
numerical methods
finite difference method
finite element method
mesh adaptation

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description: This paper is devoted to the consideration of numerical methods for solving one-dimensional problems of mathematical physics and the evaluation of the influence of adaptive mesh on the error in the calculation. Tasks that were solved in the course of the work: 1. Implementation of the finite difference method and the finite element method. 2. Obtaining solutions to problems for a uniform mesh and comparing the results of the methods. 3. Obtaining a solution to a onedimensional problem for an adaptive mesh by the finite element method, constructing an adaptive algorithm, and comparing the results obtained. Numerical experiments have shown that in the simplest cases, the results obtained by the two methods coincide, and the solution of the problem by the finite element method using an adaptive algorithm gives a significantly lower error on an adaptive mesh than on a uniform mesh with the same number of nodes.