Some aspects of numerical analysis of the fractional mathematical mcsherry model for describing an artificial ecg

Alimov, Kh.T., Parovik, R.I., Алимов, Х.Т., Паровик, Р.И.

Ҳисоблаш ва амалий математика муаммолари · 2024-yil

Annotatsiya

The article examines McSherry’s mathematical model, taking into account heredity, to describe artificial ECGs. The mathematical model consists of three ordinary nonlinear differential equations with derivatives of fractional orders in the Gerasimov-Caputo sense, for which local initial conditions are valid (Cauchy problem). The Cauchy problem is solved using a numerical method based on a nonlocal explicit finite-difference scheme of first order accuracy. The numerical algorithm was implemented in a computer program in the Maple language. Using Runge’s rule, it is shown that the order of computational accuracy of the numerical algorithm tends to the theoretical order as the number of nodes of the computational grid increases. Using a computer program, the simulation results were visualized for various values of the orders of fractional derivatives. It is shown that the orders of fractional derivatives allow a more flexible description of the artificial ECG. It should be noted that the numerical method, which was used in the article, can be applied to a more general mathematical model when the orders of fractional derivatives are functions of time.

Maqola ma’lumotlari
MualliflarAlimov, Kh.T., Parovik, R.I., Алимов, Х.Т., Паровик, Р.И.
JurnalҲисоблаш ва амалий математика муаммолари
NashriyotТошкент ахборот технологиялари университети қошидаги, Ахборот-коммуникация технологиялари илмий-инновацион, маркази
ISSN2181-8460, 2181-046X
Nashr sanasi2024-05-22
Son2
Betlar7-16
TilIngliz
Indeksga qo‘shilgan2026-08-27

Maqolaning asl sahifasi

Kalit so‘zlar

McSherry model, ECG, fractional derivative, numerical algorithm, order of accuracy, Runge’s rule, модель Макшерри, ЭКГ, дробная производная, численный алгоритм, порядок точности, правило Рунге

Iqtibos keltirish

APAAlimov, Kh.T., Parovik, R.I., Алимов, Х.Т., & Паровик, Р.И. (2024). SOME ASPECTS OF NUMERICAL ANALYSIS OF THE FRACTIONAL MATHEMATICAL MCSHERRY MODEL FOR DESCRIBING AN ARTIFICIAL ECG. Ҳисоблаш ва амалий математика муаммолари, (2), 7-16. https://journals.airi.uz/index.php/pvpm/article/view/10
GOST (OAK)Alimov, Kh.T. va b. SOME ASPECTS OF NUMERICAL ANALYSIS OF THE FRACTIONAL MATHEMATICAL MCSHERRY MODEL FOR DESCRIBING AN ARTIFICIAL ECG // Ҳисоблаш ва амалий математика муаммолари. – 2024. – № 2. – P. 7-16.
MLAAlimov, Kh.T., Parovik, R.I., Алимов, Х.Т., and Паровик, Р.И. “SOME ASPECTS OF NUMERICAL ANALYSIS OF THE FRACTIONAL MATHEMATICAL MCSHERRY MODEL FOR DESCRIBING AN ARTIFICIAL ECG.” Ҳисоблаш ва амалий математика муаммолари, (2), 7-16, 2024. https://journals.airi.uz/index.php/pvpm/article/view/10
ChicagoAlimov, Kh.T., Parovik, R.I., Алимов, Х.Т., and Паровик, Р.И. “SOME ASPECTS OF NUMERICAL ANALYSIS OF THE FRACTIONAL MATHEMATICAL MCSHERRY MODEL FOR DESCRIBING AN ARTIFICIAL ECG.” Ҳисоблаш ва амалий математика муаммолари, (2), 7-16 (2024). https://journals.airi.uz/index.php/pvpm/article/view/10
HarvardAlimov, Kh.T., Parovik, R.I., Алимов, Х.Т., and Паровик, Р.И (2024) ‘SOME ASPECTS OF NUMERICAL ANALYSIS OF THE FRACTIONAL MATHEMATICAL MCSHERRY MODEL FOR DESCRIBING AN ARTIFICIAL ECG’, Ҳисоблаш ва амалий математика муаммолари, (2), 7-16. https://journals.airi.uz/index.php/pvpm/article/view/10
BibTeX
@article{alimovkht2024,
  title = {SOME ASPECTS OF NUMERICAL ANALYSIS OF THE FRACTIONAL MATHEMATICAL MCSHERRY MODEL FOR DESCRIBING AN ARTIFICIAL ECG},
  author = {Alimov, Kh.T. and Parovik, R.I. and Алимов, Х.Т. and Паровик, Р.И.},
  journal = {Ҳисоблаш ва амалий математика муаммолари},
  year = {2024},
  number = {2},
  pages = {7-16},
  url = {https://journals.airi.uz/index.php/pvpm/article/view/10}
}

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