A new numerical scheme based on Haar wavelets for the numerical solution of the Chen–Lee–Liu equation

Abdullah, Abdullah; Rafiq, Mohd

doi:10.1016/j.ijleo.2020.165847

Cited by 7 publications

(2 citation statements)

References 36 publications

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“…This wavelet basis originated from a single function called the mother wavelet ψ(x), which is a small beat. In literature, wavelet methods such as the Euler wavelet scheme for volterra delay integral DEs [14], Hermite wavelet scheme for nonlinear singular initial value problems (IVPs) [15], Legendre wavelet method for nonlinear DDEs [16], continuous wavelet series method for Lane-Emden equations [17], B-spline method for Burgers-Huxley equation [18], Haar wavelet method for the Chen-Lee-Liu equation [19], DDEs based on Euler wavelets [20], R-K method for the DDEs [21] and A novel approach for Pantograph equations [22], and so on [23,24] have been presented.…”

Section: Introductionmentioning

confidence: 99%

Wavelets approach for the solution of nonlinear variable delay differential equations

Kumbinarasaiah

Mundewadi

2023

International Journal of Mathematics and Computer in Engineering

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In this study, the Laguerre wavelet-oriented numerical scheme for nonlinear first and second-order delay differential equations (DDEs) is offered. The proposed technique is dependent on the truncated series of the Laguerre wavelets approximation of an unknown function. Here, we transform the different ordered DDEs into a system of non-linear algebraic equations with the help of limit points of a sequence of collocation points. Four nonlinear illustrations are involved to prove the efficiency of the planned technique. Obtained results are equated with the current results, indicating the proposed technique’s accuracy and efficiency.

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Section: Introductionmentioning

confidence: 99%

Wavelets approach for the solution of nonlinear variable delay differential equations

Kumbinarasaiah

Mundewadi

2023

International Journal of Mathematics and Computer in Engineering

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“…More so, there are many various analytical and computational methods in the literature to address the class of Nonlinear Schrodinger Equations (NLSE) including among others [12][13][14][15][16][17][18][19][20][21][22][23] and the references therewith. Nevertheless, with regards to the CLL equation, very few computational techniques are available to numerically treat the model via the application of the standard Adomian's method and its modifications with particular types of soliton solutions [24][25][26][27][28][29]. Other similar numerical-based considerations to treat both the integer and non-integer order evolution equations and other broader forms of differential equations models are available in [30][31][32][33][34][35][36][37][38][39][40] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Approximate Solutions for Dark and Singular Optical Solitons of Chen-Lee-Liu Model by Adomian-based Methods

Mohammed

Bakodah

2021

Int. J. Appl. Comput. Math

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The current manuscript investigates by proposing new numerical schemes based on the Adomian's technique for the resolution of the dark and singular solutions of the Chen-Lee-Liu (CLL) equation. More precisely, the schemes are derived from the Wazwaz's modification of the Adomian's method and the improved Adomian's method for treating complex-valued evolution equations. The CLL model is applicable to a variety of applications including photonic and optical crystal fibers. The schemes which are implemented via the help of the Maple software have many salient advantages as contained in the comparative analysis. Finally, we depict certain results graphically together with some supportive tables, in addition to some comprehensive remarks.

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A computational approach for finding the numerical solution of modified unstable nonlinear Schrödinger equation via Haar wavelets

Abdullah

Rafiq

2021

Math Methods in App Sciences

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In this work, we combined the Haar wavelet collocation method with the backward Euler difference formula to determine the approximate solutions of the modified unstable nonlinear Schrödinger equation. The backward Euler difference formula estimates the time derivative term and the Haar wavelet collocation method estimate the space derivative terms of the modified unstable nonlinear Schrödinger equation. This approach reduces the modified unstable nonlinear Schrödinger equation into a finite system of linear equations. In addition, we substantiate the efficiency and accuracy of the method graphically and numerically with the help of four examples.

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A new numerical scheme based on Haar wavelets for the numerical solution of the Chen–Lee–Liu equation

Cited by 7 publications

References 36 publications

Wavelets approach for the solution of nonlinear variable delay differential equations

Wavelets approach for the solution of nonlinear variable delay differential equations

Approximate Solutions for Dark and Singular Optical Solitons of Chen-Lee-Liu Model by Adomian-based Methods

A computational approach for finding the numerical solution of modified unstable nonlinear Schrödinger equation via Haar wavelets

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