Taylor wavelet collocation method for Benjamin–Bona–Mahony partial differential equations

Shiralashetti, S. C.; Hanaji, S. I.

doi:10.1016/j.rinam.2020.100139

Cited by 10 publications

(4 citation statements)

References 25 publications

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“…Equation ( 22) is the physical representation of application reflecting in the electric locomotive faster. An important construct was the delay, which collects current from an overhead wire which can be seen in the references [1,3,7,35]. Figure 1, represents the physical behavior of numerical solution and exact solution for l = 1, P = 9, respectively at grid points and figure 2, represents the physical behavior of the absolute errors of estimated solutions for l = 1, P = 6, 9, 12, respectively at grid points.…”

Section: Numerical Examplesmentioning

confidence: 99%

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Application of Taylor Wavelets in Computation of Solution of Delay Differential Equations

Yadav

Piriadarshani

Kavitha

et al. 2022

Preprint

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In this paper, Taylor Wavelets Technique (TWT) is applied to solve delay differential equation (DDE). Convergence and error estimation are defined using TWT and examples were given to support our results in computation of DDE for several different parameters. It is indicated that the suggested method is the suitable one for obtaining solution of a different classes of DDE which have been considered in a strong manner in current areas in several field of science and engineering.

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Section: Numerical Examplesmentioning

confidence: 99%

“…The proposed technique has the capability to be expanded to all DDEs. We focus at the mentioned DDEs given by [1,2,3] v ′ (z) = a(z)v(z) + b(z)v(αz) + c(z) (1) with initial condition…”

Section: Introductionmentioning

confidence: 99%

Application of Taylor Wavelets in Computation of Solution of Delay Differential Equations

Yadav

Piriadarshani

Kavitha

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Numerical wavelet methods have gained significant attention in recent years for solving differential equations arising in diverse fields such as signal processing, image analysis and mathematical modeling. Notable contributions include the use of Laguerre wavelets [8], Taylor wavelets [9], cardinal B-splines [10], Bernoulli wavelets [11] and Hermite wavelets [12,13]. Among these, the HWM has been widely utilized due to its accuracy.…”

Section: Introductionmentioning

confidence: 99%

Effects of heat transfer on MHD suction–injection model of viscous fluid flow through Differential transformation and Hermite wavelet techniques

Raghunatha,

Y.,

2024

Scientia Iranica

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This study investigates the magnetohydrodynamic flow and heat transfer between two parallel disks, considering suction and injection effects at the disks. The governing equations describing the flow and thermal transport are derived based on the principles of mass, momentum and energy conservation for an electrically conducting fluid. As the governing partial differential equations (PDEs) are highly nonlinear, similarity transformations are applied to transform them into coupled ordinary differential equations (ODEs). Numerical techniques, namely the Hermite wavelet method (HWM) and Differential transformation technique (DTT) are then employed to solve the transformed equations. Parametric effects of several influential parameters such as the Prandtl number, squeeze number, Hartmann number, and thermophoresis parameter on the velocity and temperature profiles are systematically analyzed. Comparisons are made with previous findings in the literature. The results indicate significant dependence of flow behavior and heat transfer on the governing parameters. Velocity and temperature distributions in the boundary layer are presented and discussed in detail. The proposed mathematical model and numerical approach provide useful insights into heat transfer characteristics for parallel disk systems and similar engineering applications involving magnetohydrodynamic flows with suction or injection effects.

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“…2023, 7, 346 2 of 15 functions have been used to solve a wide range of FDEs. Legendre, Haar, Bernoulli, Euler, CAS, Taylor, Laguree, Chebyshev wavelets of first and second kind are employed in recent studies elsewhere [20][21][22][23][24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Hermite Wavelet Method for Nonlinear Fractional Differential Equations

2023

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Nonlinear fractional differential equations (FDEs) constitute the basis for many dynamical systems in various areas of engineering and applied science. Obtaining the numerical solutions to those nonlinear FDEs has quickly gained importance for the purposes of accurate modelling and fast prototyping among many others in recent years. In this study, we use Hermite wavelets to solve nonlinear FDEs. To this end, utilizing Hermite wavelets and block-pulse functions (BPF) for function approximation, we first derive the operational matrices for the fractional integration. The novel contribution provided by this method involves combining the orthogonal Hermite wavelets with their corresponding operational matrices of integrations to obtain sparser conversion matrices. Sparser conversion matrices require less computational load, and also converge rapidly. Using the generated approximate matrices, the original nonlinear FDE is converted into an algebraic equation in vector-matrix form. The obtained algebraic equation is then solved using the collocation points. The proposed method is used to find a number of nonlinear FDE solutions. Numerical results for several resolutions and comparisons are provided to demonstrate the value of the method. The convergence analysis is also provided for the proposed method.

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Taylor wavelet collocation method for Benjamin–Bona–Mahony partial differential equations

Cited by 10 publications

References 25 publications

Application of Taylor Wavelets in Computation of Solution of Delay Differential Equations

Application of Taylor Wavelets in Computation of Solution of Delay Differential Equations

Effects of heat transfer on MHD suction–injection model of viscous fluid flow through Differential transformation and Hermite wavelet techniques

Hermite Wavelet Method for Nonlinear Fractional Differential Equations

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