CD4+T Hücrelerindeki HIV Enfeksiyonunun Yayılım Modelinin Chebyshev Operasyonel Matris Metodu ile bir Nümerik Uygulaması

Yıl 2023, Cilt: 13 Sayı: 1&2, 59 - 73, 31.12.2023

Yalçın Öztürk Ayşe Anapalı Şenel Ceren Limoncu Mustafa Gülsu

https://doi.org/10.37094/adyujsci.1351204

Öz

Bu çalışma, CD4+T hücrelerinde HIV virüsünün matematiksel yayılım modeli için yaklaşık çözümler elde etmeyi amaçlamaktadır. Nümerik çözümler Chebyshev polinomları ile operasyonel matris metodunun CD4+T hücrelerinde HIV virüsünün matematiksel yayılım modeline uygulanması ile elde edilecektir. Önerilen method modele ait nümerik çözümlerin bir Chebyshev serisi formunda yazılarak, Chebyhev serisi içindeki bilinmeyen katsayıları içeren lineer olmayan bir denklem sistemi inşa atmeyi amaçlar. Yöntemin doğruluğunu kontrol etmek için nümerik sonuçlar var olan nümerik yöntemlerle karşılaştırılmıştır.

Anahtar Kelimeler

HIV Enfenksiyon Modeli, CD4+T hücreleri, Operasyonel matris metot, Chebyshev polinomları, Lineer olmayan diferansiyel denklem sistemleri

Proje Numarası

22/139/05/1

A Numerical Application of the Chebyshev Operational Matrix Method for HIV Infection of CD4+T-cells

Öz

In this research study, we aim to approximate a solution for the mathematical model of the Human Immunodeficiency Virus (HIV) infection of CD4+T-cells. An operational matrix method based on Chebyshev orthogonal polynomials has been adapted to obtain numerical solutions for the model of HIV infection of CD4+T-cells. The proposed numerical scheme is built on a system of a nonlinear algebraic equation, including coefficients of a finite Chebyshev series that represent the approximate solutions of the model. Results are compared to existing methods to verify the accuracy of the numerical scheme.

Anahtar Kelimeler

Model of the HIV infection, CD4+T cells, Operational matrix method, Chebyshev polynomials, Nonlinear system of differential equations

Destekleyen Kurum

Muğla Sıtkı Kocman University Research Projects Coordination Office

Proje Numarası

22/139/05/1

Teşekkür

Muğla Sıtkı Kocman University Research Projects Coordination Office has granted this paper. Project Grant Number 22/139/05/1 and title “Extending the Operational Matrix Method to Nonlinear System Models.”

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