Haar Wavelet Series Method for Solving Simultaneous Proportional Delay Differential Equations

Hussain, Basharat; Afroz, Afroz

doi:10.1007/978-981-19-0179-9_25

Cited by 2 publications

(2 citation statements)

References 24 publications

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“…The popularity of wavelet-based numerical algorithms in the numerical analysis may be attributed to their straightforwardness, computational simplicity, and speedy convergence. It's important to keep in mind that there are distinct wavelet families, including Chebyshev, Daubechies, B-spline, Bernoulli, Haar, Fibonacci, Ultraspherical, and Legendre wavelets are consistently used to solve various biological and physical problems [21][22][23][24][25][26][27][28][29][30]. In this paper, we introduce a unique wavelets collocation approach that solves the fractional-order population growth model using Fibonacci polynomials and wavelets as fundamental functions, as well as a quasi-linearization methodology.…”

Section: Introductionmentioning

confidence: 99%

Hybrid Fibonacci wavelet method to solve fractional‐order logistic growth model

Ahmed

Jahan

Nisar

2023

Math Methods in App Sciences

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The aim of this study is to develop the Fibonacci wavelet method together with the quasi‐linearization technique to solve the fractional‐order logistic growth model. The block‐pulse functions are employed to construct the operational matrices of fractional‐order integration. The fractional derivative is described in the Caputo sense. The present time‐fractional population growth model is converted into a set of nonlinear algebraic equations using the proposed generated matrices. Making use of the quasi‐linearization technique, the underlying equations are then changed to a set of linear equations. Numerical simulations are conducted to show the reliability and use of the suggested approach when contrasted with methods from the existing literature. A comparison of several numerical techniques from the available literature is presented to show the efficacy and correctness of the suggested approach.

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Section: Introductionmentioning

confidence: 99%

Hybrid Fibonacci wavelet method to solve fractional‐order logistic growth model

Ahmed

Jahan

Nisar

2023

Math Methods in App Sciences

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“…These techniques have made great strides in the fields of numerical analysis and approximation theory because of their low complexity, computational efficiency, and speedy convergence. Haar wavelets [16, 19], Bernoulli wavelets [20], harmonic wavelets [21], ultraspherical wavelets [22], Legendre wavelets [20], Laguerre wavelets [23], Chebyshev wavelets [17], and Euler wavelets [24] are all examples of wavelet families that are useful in addressing a wide range of physical, engineering, and biological issues [25, 26].…”

Section: Introductionmentioning

confidence: 99%

Fibonacci wavelet method for time fractional convection–diffusion equations

Yadav,

Jahan,

Nisar

2023

Math Methods in App Sciences

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This study concentrates on time fractional convection–diffusion equations (TFCDEs) with variable coefficients and their numerical solutions. Caputo derivative is used to calculate the time fractional order derivatives. In order to give an approximate solution to the TFCDE, an effective approach is proposed utilizing Fibonacci wavelet and block pulse functions. The Fibonacci wavelets operational matrices of fractional order integration are constructed. By combining the collocation technique, they are used to simplify the fractional model to a collection of algebraic equations. The suggested approach is quite practical for resolving issues of this nature. The comparison and analysis with other approaches demonstrate the effectiveness and precision of the suggested approach.

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Haar Wavelet Series Method for Solving Simultaneous Proportional Delay Differential Equations

Cited by 2 publications

References 24 publications

Hybrid Fibonacci wavelet method to solve fractional‐order logistic growth model

Hybrid Fibonacci wavelet method to solve fractional‐order logistic growth model

Fibonacci wavelet method for time fractional convection–diffusion equations

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