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Article

Fibonacci Wavelet Collocation Method for Solving Dengue Fever SIR Model

by
Amit Kumar
1,*,
Ayub Khan
2 and
Abdullah Abdullah
3
1
Department of Mathematics, Atma Ram Sanatan Dharma College, University of Delhi, New Delhi 110021, India
2
Department of Mathematics, Jamia Millia Islamia, New Delhi 110025, India
3
Department of Mathematics, Zakir Husain Delhi College, University of Delhi, New Delhi 110002, India
*
Author to whom correspondence should be addressed.
Mathematics 2024, 12(16), 2565; https://doi.org/10.3390/math12162565
Submission received: 13 July 2024 / Revised: 5 August 2024 / Accepted: 11 August 2024 / Published: 20 August 2024
(This article belongs to the Special Issue Advanced Numerical Methods for Differential Equations: Recent Developments, Analysis and Applications)
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Abstract

The main focus in this manuscript is to find a numerical solution of a dengue fever disease model by using the Fibonacci wavelet method. The operational matrix of integration has been obtained using Fibonacci wavelets. The proposed method is called Fibonacci wavelet collocation method (FWCM). This biological model has been transformed into a system of nonlinear algebraic equations by using the Fibonacci wavelet collocation scheme. Afterward, this system has been solved by using the Newton–Raphson method. Finally, we provide evidence that our results are better than those obtained by various current approaches, both numerically and graphically, demonstrating the method’s accuracy and efficiency.
Keywords: Fibonacci wavelet; Dengue Fever SIR model; collocation method; Fibonacci polynomials; system of ordinary differential equations; operational matrices Fibonacci wavelet; Dengue Fever SIR model; collocation method; Fibonacci polynomials; system of ordinary differential equations; operational matrices

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MDPI and ACS Style

Kumar, A.; Khan, A.; Abdullah, A. Fibonacci Wavelet Collocation Method for Solving Dengue Fever SIR Model. Mathematics 2024, 12, 2565. https://doi.org/10.3390/math12162565

AMA Style

Kumar A, Khan A, Abdullah A. Fibonacci Wavelet Collocation Method for Solving Dengue Fever SIR Model. Mathematics. 2024; 12(16):2565. https://doi.org/10.3390/math12162565

Chicago/Turabian Style

Kumar, Amit, Ayub Khan, and Abdullah Abdullah. 2024. "Fibonacci Wavelet Collocation Method for Solving Dengue Fever SIR Model" Mathematics 12, no. 16: 2565. https://doi.org/10.3390/math12162565

APA Style

Kumar, A., Khan, A., & Abdullah, A. (2024). Fibonacci Wavelet Collocation Method for Solving Dengue Fever SIR Model. Mathematics, 12(16), 2565. https://doi.org/10.3390/math12162565

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