Wave Propagation by Way of Exponential B-Spline Galerkin Method

Görgülü, Melis Zorşahin; Dağ, İdris; Irk, Dursun

doi:10.1088/1742-6596/766/1/012031

Cited by 7 publications

(7 citation statements)

References 12 publications

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“…We found good results even for large step sizes. It is noted that the error norms of the Galerkin cubic B-spline are lower than Explicit method [3], Implicit/explicit [3], and Split-step Fourier method [3] when we compare the results of the proposed method with those referenced in [1,4,19]. In Table 4, the results are documented for when the soliton amplitude is equal to 2.…”

Section: Single Soliton Solution To the Nls Equationmentioning

confidence: 99%

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Soliton Solution of Schrödinger Equation Using Cubic B-Spline Galerkin Method

Iqbal

Hamid

Ismail

2019

Fluids

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The non-linear Schrödinger (NLS) equation has often been used as a model equation in the study of quantum states of physical systems. Numerical solution of NLS equation is obtained using cubic B-spline Galerkin method. We have applied the Crank–Nicolson scheme for time discretization and the cubic B-spline basis function for space discretization. Three numerical problems, including single soliton, interaction of two solitons and birth of standing soliton, are demonstrated to evaluate to the performance and accuracy of the method. The error norms and conservation laws are determined and found to be in good agreement with the published results. The obtained results show that the approach is feasible and accurate. The proposed method has almost second order convergence. The linear stability of the method is performed using the Von Neumann method.

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Section: Single Soliton Solution To the Nls Equationmentioning

confidence: 99%

“…It was reported that the proposed method gave satisfactory results. The exponential B-splines Galerkin method for the numerical solution of the Burger's equation was also applied by Gorgulu et al [4].…”

Section: Introductionmentioning

confidence: 99%

Soliton Solution of Schrödinger Equation Using Cubic B-Spline Galerkin Method

Iqbal

Hamid

Ismail

2019

Fluids

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“…phenomena such as gas dynamics, fluid mechanics, traffic flow and nonlinear acoustics, is given as Various numerical and analytical solutions of this equation are available in the literature [12][13][14][15][16][17][18][19]. Various noble methods were developed to numerically solve Fisher's reaction-diffusion equation shown in the papers [20][21][22].…”

Section: Introductionmentioning

confidence: 99%

A fourth-order B-spline collocation method for nonlinear Burgers–Fisher equation

2020

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A fourth-order B-spline collocation method has been applied for numerical study of Burgers-Fisher equation, which illustrates many situations occurring in various fields of science and engineering including nonlinear optics, gas dynamics, chemical physics, heat conduction, and so on. The present method is successfully applied to solve the Burgers-Fisher equation taking into consideration various parametric values. The scheme is found to be convergent. Crank-Nicolson scheme has been employed for the discretization. Quasi-linearization technique has been employed to deal with the nonlinearity of equations. The stability of the method has been discussed using Fourier series analysis (von Neumann method), and it has been observed that the method is unconditionally stable. In order to demonstrate the effectiveness of the scheme, numerical experiments have been performed on various examples. The solutions obtained are compared with results available in the literature, which shows that the proposed scheme is satisfactorily accurate and suitable for solving such problems with minimal computational efforts.

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“…Numerical solutions of this equation, used in modelling the solitary wave and travelling waves, have been studied by the researchers due to the limitations in analytical solutions. Numerical solutions, which have been investigated recently, have been obtained by least squares, splitting, homotopy perturbation, finite difference and quadrature methods [3][4][5][6][7][8][9][10]. In parallel with these studies, we used the quintic B-spline collocation method for space and the various-order single step methods for time discretization that were not implemented before.…”

Section: Introductionmentioning

confidence: 99%

A High-Order Accurate Numerical Algorithm for the Numerical Solution of Burgers’ Equation

Görgülü

2019

Muş Alparslan Üniversitesi Fen Bilimleri Dergisi

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In this study, a high accurate numerical solution of the Burgers' equation is obtained. For this, the collocation method based on quintic B-spline functions for space discretization and the fourth-order single step method for time discretization are used. In order to see the efficiency of the algorithm, a test problem with an analytical solution is discussed and compared with the numerical solution obtained.

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Wave Propagation by Way of Exponential B-Spline Galerkin Method

Cited by 7 publications

References 12 publications

Soliton Solution of Schrödinger Equation Using Cubic B-Spline Galerkin Method

Soliton Solution of Schrödinger Equation Using Cubic B-Spline Galerkin Method

A fourth-order B-spline collocation method for nonlinear Burgers–Fisher equation

A High-Order Accurate Numerical Algorithm for the Numerical Solution of Burgers’ Equation

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