Fibonacci wavelet method for the numerical solution of a fractional relaxation–oscillation model

Jahan, Shah; Ahmed, Shahid; Yadav, Pooja; Nisar, Kottakkaran Sooppy

doi:10.1016/j.padiff.2023.100568

Cited by 6 publications

(2 citation statements)

References 33 publications

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“…In this Section, Numerical simulations are carried to evaluate how accurate and dependable the method is. Recently, Mathematical modelling has been investigated with Numerical simulations [24][25][26]. The Mathematical expressions derived in this paper have been cross-referenced with a highly precise numerical solution acquired through MATLAB (pdex4) software.…”

Section: Comparison Of Analytical Results With Numerical Simulationmentioning

confidence: 99%

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Investigation of a Mathematical Model and Non-Linear Effects Based on Parallel-Substrates Biochemical Conversion

et al. 2024

Contemp. Math.

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According to the broad applicability and advancements made in addressing complex non-linear problems, Researchers have been actively involved in addressing the accurate approaches to solve non-linear problems in fields such as chemical science, material science, and image processing. In this paper, the Amperometric response of catalase-peroxidase (parallel-substrates) conversion has been discussed. The Mathematical model relies on a set of non-linear differential equations that describe the reaction and diffusion of the system. The analytical methods were extended to derive the approximate solution of the non-linear reaction-diffusion equation. The straightforward and concise analytical expressions for the concentrations and current of the Biosensor are developed. This study includes the computational resolution of the problem by utilizing a MATLAB program. A comparison between analytical outcomes and those derived numerically has been conducted. The analytical findings presented are dependable and offer an effective comprehension of the behaviour of this system.

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Section: Comparison Of Analytical Results With Numerical Simulationmentioning

confidence: 99%

“…The Biosensor's present reaction is reliant on the concentration of the product (P 1 ). The analytical derivation provides the equation for the dimensionless current as expressed in Eqn (24). The current generated by the Biosensor is independent on the reaction rate.…”

Section: Resultsmentioning

confidence: 99%

Investigation of a Mathematical Model and Non-Linear Effects Based on Parallel-Substrates Biochemical Conversion

et al. 2024

Contemp. Math.

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A Study of Fractional Order Financial Crime Model Using the Gegenbauer Wavelet Collocation Method

2024

Advcd Theory and Sims

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The manuscript investigates the numerical approximation of the fractional mathematical model of the financial crime population dynamics by the Gegenbauer wavelet collocation method. The study aims to enhance the accuracy and efficiency of solving the underlying differential equations that describe these phenomena by utilizing the proposed technique. The financial crime model is a nonlinear coupled system of ordinary differential equations. Using the Gegenbauer wavelets, the novel operational matrices of integration are created. A nonlinear system of ordinary differential equations are transformed into a system of algebraic equations using the characteristics of the Gegenbauer wavelet expansions and the operational matrix of integration, which speeds up processing. Then, this system of algebraic equations is solved using the Newton‐iterative technique to find the unknown Gegenbauer coefficients that help to obtain the approximate solution for the system. A numerical illustration is presented to show the efficacy and precision of the approach. The numerical results obtained from the projected approach are compared with the existing methods, such as NDSolve and Runge Kutta methods. These results show that the projected scheme is simple, reliable, and resilient. The findings suggest that this approach can be a powerful tool for researchers and practitioners in the financial sector, aiding in developing crime prevention and intervention strategies. The study concludes with suggestions for future research directions.

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On computational analysis via fibonacci wavelet method for investigating some physical problems

Ahmed,

Jahan,

Shah

et al. 2024

J. Appl. Math. Comput.

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In this work, we considered wavelet analysis and the application of the Fibonacci wavelet collocation method (FWCM) for solving partial differential equations (PDEs). The proposed technique starts with formulating Fibonacci wavelets using Fibonacci polynomials. Subsequently, the spectral collocation technique is applied to convert the given problem into a system of algebraic equations, which are then solved using the Newton method. Error estimation and convergence analysis of the proposed scheme are also investigated. The effectiveness and precision of the FWCM are demonstrated through a comparative analysis with exact solutions and other existing methods in the literature. The obtained results demonstrate that the proposed technique is an efficient tool for solving PDEs and is also applicable for numerically examining similar types of physical problems.

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Fibonacci wavelet method for the numerical solution of a fractional relaxation–oscillation model

Cited by 6 publications

References 33 publications

Investigation of a Mathematical Model and Non-Linear Effects Based on Parallel-Substrates Biochemical Conversion

Investigation of a Mathematical Model and Non-Linear Effects Based on Parallel-Substrates Biochemical Conversion

A Study of Fractional Order Financial Crime Model Using the Gegenbauer Wavelet Collocation Method

On computational analysis via fibonacci wavelet method for investigating some physical problems

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