Creation of Software for Numerical Solution of Fractional Diffusion Equation

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dc.creatorKarimov, M.M.
dc.creatorYaxshiboyev, M.U.
dc.date2023-12-26
dc.date.accessioned2024-03-25T11:46:37Z
dc.date.available2024-03-25T11:46:37Z
dc.descriptionIn this article, descriptions of partial fractional derivatives in the sense of Riemann-Liouville and Caputo, brief descriptions of the literature describing a number of methods for obtaining approximate solutions to fractional partial differential equations are given. An algorithm for the numerical solution of a non-homogeneous Caputo fractional diffusion equation by the finite difference method based on implicit calculation schemes is described. Based on the calculation algorithm, the software was designed using the object-oriented design method. The project is developed in the form of one main class. The class project is represented in a special diagram. Using the software developed on the basis of the project, a numerical solution for the special case of the fractional diffusion equation in the sense of Caputo was created. In a three-dimensional coordinate system, a set of numerical solutions is represented in a three-dimensional graphic form.en-US
dc.descriptionMazkur maqolada Riman-Liuvill va Kaputo ma’nosidagi xususiy kasr hosilalar tavsiflari, kasr tartibli xususiy hosilali differensial tenglamalarning taqribiy yechimlarini olish uchun bir qancha sonli usullar bayon qilingan adabiyotlarning qisqacha tavsiflari keltirib o‘tilgan. Bir jinsli bo‘lmagan Kaputo ma’nosidagi kasr tartibli diffuziya tenglamasini oshkormas hisoblash sxemalariga asoslangan chekli ayirmalar usuli boʻyicha sonli yechishning algoritmi bayon qilingan. Hisoblash algoritmi asosida obyektga yo‘naltirilgan loyihalash usulidan foydalangan holda dasturiy vosita loyihalangan. Loyiha bitta asosiy sinf shaklida ishlab chiqilgan. Sinf loyihasi maxsus digramma ko‘rinishda ifodalangan. Loyiha asosida ishlab chiqilgan dasturiy vositadan foydalanilgan holda Kaputo ma’nosidagi kasr tartibli diffuziya tenglamasining xususiy holi uchun sonli yechimi hosil qilingan. Uch o‘lchamli koordinatalar tizimida sonli yechimlar toʻplami uch o‘lchovli grafik ko‘rinishda tasvirlangan.ru-RU
dc.formatapplication/pdf
dc.identifierhttps://ijdt.uz/index.php/ijdt/article/view/130
dc.identifier10.62132/ijdt.v6i4.130
dc.identifier.urihttps://dspace.umsida.ac.id/handle/123456789/36085
dc.languagerus
dc.publisherSamarkand branch of TUITru-RU
dc.relationhttps://ijdt.uz/index.php/ijdt/article/view/130/84
dc.rightsCopyright (c) 2023 Каримов М.М.ru-RU
dc.rightshttps://creativecommons.org/licenses/by/4.0ru-RU
dc.sourceINTERNATIONAL JOURNAL OF THEORETICAL AND APPLIED ISSUES OF DIGITAL TECHNOLOGIES; Vol. 6 No. 4 (2023): International Journal of Theoretical and Applied Issues of Digital Technologies; 29-35en-US
dc.sourceМеждународный Журнал Теоретических и Прикладных Вопросов Цифровых Технологий; Том 6 № 4 (2023): Международный журнал теоретических и прикладных вопросов цифровых технологий; 29-35ru-RU
dc.source2181-3094
dc.source2181-3086
dc.subjectCaputo-type derivativeen-US
dc.subjectCaputo-type fractional time diffusion equationen-US
dc.subjectcentral finite difference schemeen-US
dc.subjectKaputo ma’nosidagi hosilaru-RU
dc.subjectKaputo ma’nosidagi vaqt boʻyicha kasr tartibli diffuziya tenglamasiru-RU
dc.subjectmarkaziy chekli ayirmali sxemaru-RU
dc.titleCreation of Software for Numerical Solution of Fractional Diffusion Equationen-US
dc.titleKasr tartibli diffuziya tenglamasini sonli yechishning dasturiy vositasini yaratishru-RU
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:eu-repo/semantics/publishedVersion
dc.typeРецензированная статьяru-RU
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