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Journals / Cumhuriyet Science Journal / 2019 / Cilt: 40 - Sayı: 2

Analysis of a Random Zeeman Heartbeat Model with Differential Transformation Method

Diferansiyel Dönüşüm Yöntemi İle Rastgele Kalp Atış Modelinin Analizi

Mehmet MERDAN
Zafer BEKİRYAZICI
Pınar ORAL
Pages
285–298
Publication Date
2022-10-12
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The approximate formulas are also modified by using Laplace-Padé Method to increase the convergence interval of the approximations.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, the differential transformation method is used to examine the random Zeeman Heartbeat Model.
📊
Key Findings & Data:Some of the parameters and the initial conditions of the model are taken as random variables with Beta and Normal distributions, respectively.
💡
Conclusion & Impact:The approximate formulas are also modified by using Laplace-Padé Method to increase the convergence interval of the approximations.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper, the differential transformation method is used to examine the random Zeeman Heartbeat Model. Some of the parameters and the initial conditions of the model are taken as random variables with Beta and Normal distributions, respectively. The approximate analytical solution of the random Zeeman Model is obtained and used to find the expectation and variance of the model components. The results from the random models including Beta and normal distributed random effects are compared and the approximate numerical characteristics are obtained for these cases. The approximate formulas are also modified by using Laplace-Padé Method to increase the convergence interval of the approximations.

Özet

Bu çalışmada, rastgele Zeeman Kalpatış Modelinin incelenmesi için diferansiyel dönüşüm yöntemi kullanılmıştır. Modelin bazı parametreleri ve başlangıç koşulları sırasıyla Beta ve Normal dağılımlara sahip rastgele değişkenler olarak alınmıştır. Rastgele Zeeman Modelinin yaklaşık analitik çözümü elde edilmiş ve model bileşenlerinin beklenen değer ve varyansı elde edilmiştir. Beta ve normal olarak dağılmış rastgele etkiler altında, rastgele modellerin sonuçları karşılaştırılmış ve bu durumlar için elde edilen yaklaşık sayısal karakteristikler karşılaştırılmıştır. Elde edilen yaklaşık formüllere, yaklaşımların yakınsama aralığını artırmak için Laplace-Padé Metodu uygulanarak iyileştirilmiş çözümler bulunmuştur.

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Cite This Article

MERDAN, M., BEKİRYAZICI, Z., ORAL, P. (2022). Analysis of a Random Zeeman Heartbeat Model with Differential Transformation Method. Cumhuriyet Science Journal, Cilt: 40 - Sayı: 2, 285–298. https://ajindex.com/articles/477837

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