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Fibonacci wavelet collocation method for the numerical approximation of fractional order Brusselator chemical model

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Abstract

This research study’s primary goal is to create an efficient wavelet collocation technique to resolve a kind of nonlinear fractional order systems of ordinary differential equations that arise in the modeling of autocatalytic chemical reaction problems. Here, we created the functional matrix of integration for the Fibonacci wavelets. The Fibonacci wavelet collocation method is employed to find the numerical solution of the system of nonlinear coupled ordinary differential equations of both integer and fractional order. The nonlinear Brusselator system is transformed into an algebraic equation system using the operational matrices of fractional derivative and collocation technique. These algebraic equations are treated by the Newton–Raphson method, and obtained unknown coefficient values are substituted in the approximation. We demonstrate our method’s computational effectiveness and accuracy using different model constraints in the numerical examples. The effectiveness and consistency of the developed strategy’s performance are shown in graphs and tables. Comparisons with existing methods available in the literature demonstrate the high accuracy and robustness of the developed Fibonacci wavelet collocation method. Mathematical software Mathematica has been used to perform all calculations.

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Acknowledgements

Dr. Kumbinarasaiah S expresses his affectionate thanks to the DST-SERB, Govt. of India. New Delhi for the financial support under Empowerment and Equity Opportunities for Excellence in Science for 2023–2026. F. No. EEQ/2022/620 Dated: 07/02/2023.

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  1. Department of Mathematics, Bangalore University, Bengaluru, 560 056, India

    G. Manohara & S. Kumbinarasaiah

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  1. G. Manohara
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KS proposed the main idea of this paper. KS and MG prepared the manuscript and performed all the steps of the proofs in this research. Both authors contributed equally and significantly to writing this paper. Both authors read and approved the final manuscript.

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Manohara, G., Kumbinarasaiah, S. Fibonacci wavelet collocation method for the numerical approximation of fractional order Brusselator chemical model. J Math Chem (2023). https://doi.org/10.1007/s10910-023-01521-4

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