Kasr tartibli diffuziya tenglamasini sonli yechishning dasturiy vositasini yaratish
Боковая панель статьи
Основное содержимое статьи
Аннотация
Mazkur 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.
Информация о статье
Это произведение доступно по лицензии Creative Commons «Attribution» («Атрибуция») 4.0 Всемирная.
Библиографические ссылки
Pskhu A.V. Uravneniya v chastnykh proizvodnykh drobnogo poryadka. M.: Nauka. 2005.
Uchaykin V.V. Metod drobnykh proizvodnykh. Ul'yanovsk: Artishok, 2008. — 512 s.
Gorenflo R., Mainardi F. Fractional calculus: integral and differential equations of fractional order, Fractal and Fractional Calculus in Continuum Mechanics (Udine, 1996). CISM Courses and Lectures. 1997. Vol. 378. P. 223-276.
Podlubny I. Fractional Differential Equations. SanDiego: Academic Press. 1999.
Samko S.G., Kilbas A.A., Marichev O.I. Integraly i proizvodnyye drobnogo poryadka i nekotoryye ikh prilozheniya. Minsk: Nauka i tekhnika. 1987. 688 s.
Daraghmeh A., Qatanani N., Saadeh A. Numerical Solution of Fractional Differential Equations. Applied Mathematics, 2020, 11, 1100-1115.
Hilfer R. (Ed.) Applications of Fractional Calculus in Physics. Singapore: WSPC. 2000.
Kilbas A.A., Srivastava H.M., Trujillo J.J. Theory and Applications of Fractional Differential Equations. Amsterdam: Elsevier, 2006. —524 pages.
Metzler R., Klafter J. The random walks guide to anomalous diffusion: a fractional dynamics approach. Phys. Reports. 2000. Vol. 339. P. 1-77.
Zhang Y. A finite difference method for fractional partial differential equations. Appl. Math. Comput., 215 (2009), pp. 524-529.
Scherera R., Kallab Sh.L., Tangc Y., Huang J. The Grünwald–Letnikov method for fractional differential equations. Computers and Mathematics with Applications 62 (2011) 902–917.
Rahaman M.M., Sikdar M.M.H., Hossain M.B., Rahaman M.A., Hossain M.J. Numerical Solution of Diffusion Equation by Finite Difference Method. Journal of Mathematics (Volume 11, Issue 6 Ver. IV (Nov. - Dec. 2015), pp. 19-25.
Burden R.L., Faires J.D. Numerical Analysis, Ninth Edition. Brooks/Cole 20 Channel Center Street Boston, MA 02210, USA, 2011.
Linge S., Langtangen H.P. Finite Difference Computing with PDEs. A Modern Software Approach. Springer Cham, 2017.
Johansson R. Numerical Python: Scientific Computing and Data Science Applications with Numpy, SciPy and Matplotlib, second edition, Urayasu-shi, Chiba, Japan, 2019.
Linge S., Langtangen H.P. Programming for Computations – Python. A Gentle Introduction to Numerical Simulations with Python 3.6, Second Edition, Springer Cham, 2020.
Diethelm K., “An algorithm for the numerical solution of differential equations of fractional order,” Electronic Transactions on Numerical Analysis, vol. 5, pp. 1–6, 1997.
Kumar R. Mastering Data Analysis with Python. A Comprehensive Guide to NumPy, Pandas, and Matplotlib. Jamba Academy, USA, First Printing Edition, 2023.
Craig L. Applying UML and Patterns: An Introduction to Object-Oriented Analysis and Design and Iterative Development, Third Edition. Addison Wesley Professional, 2004.