Spectral methods using Legendre wavelets for nonlinear Klein<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si48.gif" display="inline" overflow="scroll"><mml:mo>∖</mml:mo></mml:math>Sine-Gordon equations

Yin, Fukang; Tian, Tian; Song, Junqiang; Zhu, Min

doi:10.1016/j.cam.2014.07.014

Cited by 45 publications

(23 citation statements)

References 23 publications

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“…In the works, 7,18,26-33 a wide array of numerical methods such as the finite element method (FEM), the finite difference method (FDM), and the boundary element method (BEM) have been applied to the numerical solution of the SG equation. In addition to these methods, Spectral methods [36][37][38] are playing their roles and helping to represent solutions for SG equation. 34 The reliability of these methods relies on the ability to construct and retain meshes of sufficient quality in the process of computation.…”

Section: History Of Solving Nonlinear Sg Equationsmentioning

confidence: 99%

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Generalized Lagrange Jacobi‐Gauss‐Lobatto vs Jacobi‐Gauss‐Lobatto collocation approximations for solving (2 + 1)‐dimensional Sine‐Gordon equations

Latifi

Delkhosh

2019

Math Methods in App Sciences

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The Sine-Gordon (SG) equations are very important in that they can accurately model many essential physical phenomena. In this paper, the Jacobi-Gauss-Lobatto collocation (JGL-C) and Generalized Lagrange Jacobi-Gauss-Lobatto collocation (GLJGL-C) methods are adopted and compared to simulate the (2 + 1)-dimensional nonlinear SG equations. In order to discretize the time variable t, the Crank-Nicolson method is employed. For the space variables, two numerical methods based on the aforementioned collocation methods are applied. Furthermore, error estimation for both methods is provided. The present numerical method is truly effective, free of integration and derivative, and easy to implement. The given examples and the results assert that the GLJGL-C method outperforms the JGL-C method in terms of computation speed. Also, the presented methods are very valid, effective, and reliable.

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Section: History Of Solving Nonlinear Sg Equationsmentioning

confidence: 99%

“…Bratsos 6 presented a three-time level finite-difference scheme based on the fourth order in time and second order in space approximation. In addition to these methods, Spectral methods [36][37][38] are playing their roles and helping to represent solutions for SG equation.…”

Section: History Of Solving Nonlinear Sg Equationsmentioning

confidence: 99%

Generalized Lagrange Jacobi‐Gauss‐Lobatto vs Jacobi‐Gauss‐Lobatto collocation approximations for solving (2 + 1)‐dimensional Sine‐Gordon equations

Latifi

Delkhosh

2019

Math Methods in App Sciences

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“…Due to this, many authors have found the numerical solution for the diverse class of linear and nonlinear differential and integral equations describing various physical and biological phenomena arisen in daily life using different wavelets based methods. Particularly, Haar wavelet [6,11], Legendre wavelet [27], Laguerre wavelet [24], Hermite wavelet [23] and many others. Among distinct families of wavelets, recently many mathematicians and physicists considered Chebyshev wavelets in order to analyze various model, and proved that the projected wavelets simulates and exemplifies very interesting properties of nonlinear problems in accurate and more efficient manner [22,26].…”

Section: Introductionmentioning

confidence: 99%

Chebyshev wavelets approach for the squeeze film lubrication of long porous journal bearings with couple stress fluids

Shiralashetti¹,

Praveenkumar²

2020

Malaya J. Mat.

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In the present investigation, Chebyshev wavelet-based technique is considered for the study of the effect of couple stress fluid on the squeeze film lubrication in long porous journal bearings. In order to study the pressure distribution, the non-dimensional Reynolds equation is solved by the aid of projected technique. The response of obtained solution with respect to pressure and circumferential coordinate are captured. Further, the physical behaviour of pressure with the help of eccentricity ratio, permeability parameter, and couple stress parameter is analysed and presented in terms of plots. According to results obtained, the couple stress fluid effect significantly increases the pressure as compare to the Newtonian case. Also, when the permeability parameter is decreased and the corresponding pressure decreases as compared to the solid case.

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“…It is used to describe the free particle wave function. Many numerical methods, including finite difference methods [1][2][3][4], finite element methods [5] and spectral methods [6,7], have been proposed to solve the Klein-Gordon equation. In particular, the authors in [2] proposed a simple second order centered difference in time and space, an explicit scheme to solve the Klein-Gordon equation.…”

Section: Introductionmentioning

confidence: 99%

“…In [6], a pseudo-spectral method was proposed for the spatial discretization, and Crank-Nicolson or leap-frog method was used for the temporal discretization. In [7], Legendre wavelets incorporated with a spectral method were used to solve Klein-Gordon and Sine-Gordon equations. As far as the family of finite element methods is concerned, Ref.…”

Section: Introductionmentioning

confidence: 99%

High-Order Energy and Linear Momentum Conserving Methods for the Klein-Gordon Equation

Yang

2018

Mathematics

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The Klein-Gordon equation is a model for free particle wave function in relativistic quantum mechanics. Many numerical methods have been proposed to solve the Klein-Gordon equation. However, efficient high-order numerical methods that preserve energy and linear momentum of the equation have not been considered. In this paper, we propose high-order numerical methods to solve the Klein-Gordon equation, present the energy and linear momentum conservation properties of our numerical schemes, and show the optimal error estimates and superconvergence property. We also verify the performance of our numerical schemes by some numerical examples.

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Spectral methods using Legendre wavelets for nonlinear Klein∖Sine-Gordon equations

Cited by 45 publications

References 23 publications

Generalized Lagrange Jacobi‐Gauss‐Lobatto vs Jacobi‐Gauss‐Lobatto collocation approximations for solving (2 + 1)‐dimensional Sine‐Gordon equations

Generalized Lagrange Jacobi‐Gauss‐Lobatto vs Jacobi‐Gauss‐Lobatto collocation approximations for solving (2 + 1)‐dimensional Sine‐Gordon equations

Chebyshev wavelets approach for the squeeze film lubrication of long porous journal bearings with couple stress fluids

High-Order Energy and Linear Momentum Conserving Methods for the Klein-Gordon Equation

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