title: ÐÑÐµÐ½ÐºÐ° Ð¿Ð¾ÑÑÐ´ÐºÐ° ÑÐ¾ÑÐ½Ð¾ÑÑÐ¸ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÑ ÐºÐ¾Ð½ÐµÑÐ½Ð¾-ÑÐ°Ð·Ð½Ð¾ÑÑÐ½ÑÑ ÑÑ ÐµÐ¼ Ð½Ð° Ð¿ÑÐ¸Ð¼ÐµÑÐµ ÑÐµÑÑÐ¾Ð²ÑÑ Ð·Ð°Ð´Ð°Ñ Ð½ÐµÐ¹ÑÑÐ¾Ð½Ð½Ð¾Ð¹ ÐºÐ¸Ð½ÐµÑÐ¸ÐºÐ¸
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Evaluation of the order of accuracy of various finite-difference schemes on the example of test problems of neutron kinetics
Creators: name: ÐÑÐ·Ð½ÐµÑÐ¾Ð²Ð°, ÐÐ°ÑÑÑ
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: 2024
Subjects: ÐºÐ¾Ð½ÐµÑÐ½Ð¾-ÑÐ°Ð·Ð½Ð¾ÑÑÐ½Ð°Ñ ÑÑ ÐµÐ¼Ð°
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ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
finite-difference scheme
order of accuracy
delayed neutron precursor concentration equation
diffusion equation
programme
nuclear reactor
numerical method
numerical methods
spatially distributed neutron kinetics
Euler method
numerical simulation

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð¿Ð¾ÑÑÐ´ÐºÐ° ÑÐ¾ÑÐ½Ð¾ÑÑÐ¸ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÑ ÑÐ¸ÑÐ»ÐµÐ½Ð½ÑÑ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² Ð¸ ÑÐ°Ð·Ð½Ð¾ÑÑÐ½ÑÑ ÑÑÐµÐ¼. Ð¦ÐµÐ»ÑÑ ÑÐ°Ð±Ð¾ÑÑ Ð±ÑÐ»Ð¾ Ð¿Ð¾Ð´ÑÐ²ÐµÑÐ´Ð¸ÑÑ Ð¿Ð¾ÑÑÐ´Ð¾Ðº ÑÐ¾ÑÐ½Ð¾ÑÑÐ¸ ÑÐ¸ÑÐ»ÐµÐ½Ð½ÑÑ Ð¼ÐµÑÐ¾Ð´Ð¾Ð², Ð¿ÑÐ¾Ð²ÐµÑÑÐ¸ Ð¸Ñ Ð°Ð½Ð°Ð»Ð¸Ð· Ð¸ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ. ÐÐ»Ñ ÑÑÐ¾Ð³Ð¾ ÑÑÐµÐ±Ð¾Ð²Ð°Ð»Ð¾ÑÑ Ð¿ÑÐ¾Ð²ÐµÑÑÐ¸ Ð´Ð¸ÑÐºÑÐµÑÐ¸Ð·Ð°ÑÐ¸Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹ Ð¿ÑÐ¾ÑÑÑÐ°Ð½ÑÑÐ²ÐµÐ½Ð½Ð¾-ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð½Ð¾Ð¹ ÐºÐ¸Ð½ÐµÑÐ¸ÐºÐ¸, Ð¸Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ Ð¸ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ. ÐÑÐ»Ð¸ Ð²ÑÐ²ÐµÐ´ÐµÐ½Ñ ÐºÐ¾ÑÑÑÐ¸ÑÐ¸ÐµÐ½ÑÑ Ð´Ð»Ñ ÑÐ½Ð¸Ð²ÐµÑÑÐ°Ð»ÑÐ½Ð¾Ð³Ð¾ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ ÐºÐ¾Ð½ÑÐµÐ½ÑÑÐ°ÑÐ¸Ð¸ Ð¿ÑÐµÐ´ÑÐµÑÑÐ²ÐµÐ½Ð½Ð¸ÐºÐ¾Ð² Ð·Ð°Ð¿Ð°Ð·Ð´ÑÐ²Ð°ÑÑÐ¸Ñ Ð½ÐµÐ¹ÑÑÐ¾Ð½Ð¾Ð², Ð° ÑÐ°ÐºÐ¶Ðµ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ Ð´Ð¸ÑÑÑÐ·Ð¸Ð¸. ÐÑÐ¾Ð¼Ðµ ÑÑÐ¾Ð³Ð¾ Ð±ÑÐ»Ð¾ Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð¾ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð¸ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ ÑÐ¾ÑÐ½Ð¾ÑÑÐ¸ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÑ ÑÐ¸ÑÐ»ÐµÐ½Ð½ÑÑ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² Ð¸ Ð¸Ð·Ð¼ÐµÐ½ÐµÐ½Ð¸Ðµ Ñ ÑÐµÑÐµÐ½Ð¸ÐµÐ¼ Ð²ÑÐµÐ¼ÐµÐ½Ð¸. ÐÑÐ»Ð° Ð¼Ð¾Ð´Ð¸ÑÐ¸ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð° Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð° Ð´Ð»Ñ ÑÐ°ÑÑÐµÑÐ° â Ð²Ð½ÐµÐ´ÑÐµÐ½ Ð¼ÐµÑÐ¾Ð´ Ð­Ð¹Ð»ÐµÑÐ°.
description: This work is devoted to the study of the order of accuracy of various numerical methods and difference schemes. The aim of the work was to confirm the order of accuracy of numerical methods, to analyse and compare them. This required discretisation of the equations of spatially distributed kinetics, their comparison and modelling. The coefficients for the universal delayed neutron precursor concentration equation as well as the diffusion equation were derived. In addition, the accuracy of different numerical methods and the change over time were modelled and compared. The calculation programme was modified - the Euler method was introduced.