A high resolution Hermite wavelet technique for solving space–time-fractional partial differential equations

Faheem, Mo; Khan, Arshad; Raza, Akmal

doi:10.1016/j.matcom.2021.12.012

Cited by 21 publications

(11 citation statements)

References 34 publications

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“…An efficient Hermite wavelet based high resolution method is proposed for solving space-time-fractional partial differential equations (STFPDE) in Faheem et al [1]. A fractional integral operator for Hermite wavelets is utilized and a comparative study of the numerical results with those obtained from other methods validates the authenticity of the proposed method.…”

Section: Introductionmentioning

confidence: 96%

“…Kumbinarasaiah [9] has developed an efficient modus of Hermite wavelets collocation method (HWCM) and fractional derivatives of functions for obtaining solutions of multi-term fractional differential equations (MTFDEs). An improved high resolution method based on Hermite wavelets is described in Faheem et al [10] for finding solutions of spacetime-fractional partial differential equations (STFPDE). Kumbinarasaiah & Mundewadi [11] have designed a computationally attractive method based on Hermite wavelet and operational matrix of integration and applied it to solve first-order linear and nonlinear integro-differential equations with the initial condition.…”

Section: Introductionmentioning

confidence: 99%

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Comprehensive review of numerical schemes based on Hermite wavelets

Kaur¹,

Singh²

2022

World J. Adv. Res. Rev.

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Differential and integral equations are encountered in many applications of science and engineering and many mathematical models have also been formulated in terms of these equations. Due to some shortcomings of the already existing numerical methods, researchers are making efforts to find more efficient alternatives for obtaining solutions of many practical and physical problems giving rise to differential or integral equations. As a result, wavelet methods have found their way for the numerical solution of the resulting different kinds of equations. So this review paper intends to provide the great utility, accuracy and employability of Hermite wavelets to address situations of various areas of applied mathematics, physics, biology, optimal control systems, communication theory, queuing theory, medicine and many other scientific and engineering problems.

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Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Comprehensive review of numerical schemes based on Hermite wavelets

Kaur¹,

Singh²

2022

World J. Adv. Res. Rev.

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“…This technique performs better than the present approaches in this regard. An effective high-resolution Hermite wavelet-based method is provided by Faheem et al [15] for solving space-time-fractional partial differential equations (STFPDE). Hermite wavelets were employed by Shiralashetti and Kumbinarasaih [16] as an operational matrix of integration to resolve nonlinear singular initial value issues.…”

Section: Introductionmentioning

confidence: 99%

“…A relatively young and developing area of mathematics is wavelet theory. Numerous highly nonlinear and fractional differential equations that govern mathematical models in science and engineering have recently been approximated using orthogonal and orthonormal functions, as well as wavelets [14][15][16][17][18][19][20][21][22][23][24][25][26][27]. Wavelets are being utilized more often to study issues with high computational complexity.…”

Section: Introductionmentioning

confidence: 99%

A new analytical strategy based on a wavelet computing technique for solving Fokker-Plank equation arises in stochastic phenomena

Rajaraman

Hariharan

2023

Preprint

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A relatively recent method called the Hermite Wavelet Method (HWM) is used to design a simple strategy for solving the Fokker-Planck equation (FPE) for a given pair of drift and diffusion functions in stochastic phenomena. The Fokker-Plank equation is analyzed for Morse, Hulthen and logarithmic potentials. The joint and marginal probability density functions of FPE are obtained. The strategy is efficient to apply to many linear and nonlinear problems and can significantly reduce computing labour. To demonstrate the applicability and effectiveness of the approach and to obtain the probability distribution functions of FPE, illustrative examples are provided. Mathematical subject classification: 35K20

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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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A high resolution Hermite wavelet technique for solving space–time-fractional partial differential equations

Cited by 21 publications

References 34 publications

Comprehensive review of numerical schemes based on Hermite wavelets

Comprehensive review of numerical schemes based on Hermite wavelets

A new analytical strategy based on a wavelet computing technique for solving Fokker-Plank equation arises in stochastic phenomena

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

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