A New Efficient Method for Solving Two-Dimensional Burgers' Equation

Aminikhah, Hossein

doi:10.5402/2012/603280

Cited by 7 publications

(3 citation statements)

References 13 publications

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“…To find approximate solutions to Burgers equations, several numerical schemes have been developed, including the spline FEM, ADM, Douglas FD scheme, exact explicit FDM, VIM, and others [3][4][5][6][7][8][9][10]. However, only a few analytical methods, such as the LHPM [11], Hopf-Cole Transformation [12], etc., have been developed to obtain the precise solution of certain PDEs. Laplace transform-based methods are extensively employed in mathematics to solve differential equations.…”

Section: Introductionmentioning

confidence: 99%

Solutions of (2+1)-D & (3+1)-D Burgers Equations by New Laplace Variational Iteration Technique

Singh

Singh²,

AlDerea

et al. 2023

Axioms

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The new Laplace variational iterative method is used in this research for solving the (2+1)-D and (3+1)-D Burgers equations. This technique relies on the modified variational iteration method and the Laplace transform. To apply this approach, the differential problem is first transformed into an algebraic form using the Laplace transform, and then the algebraic equations are iteratively solved using the modified variational iterative approach. By utilizing this technique, the Burgers equations can be solved both numerically and analytically. The study demonstrates the effectiveness of the new Laplace variational iterative approach through three specific examples.

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Section: Introductionmentioning

confidence: 99%

Solutions of (2+1)-D & (3+1)-D Burgers Equations by New Laplace Variational Iteration Technique

Singh

Singh²,

AlDerea

et al. 2023

Axioms

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“…Zhu et al [29] anticipated the discrete Adomian Decomposition Method in order to obtain the numerical approximation of the 2D coupled Burgers' equation. Hossein [30] proposed a scheme of new hybrid Laplace and New Homotopy Perturbation Method (LTNHPM) to solve the 2D coupled Burgers' equation.…”

Section: Introductionmentioning

confidence: 99%

A Numerical Approximation of 2D Coupled Burgers’ Equation Using Modified Cubic Trigonometric B-Spline Differential Quadrature Method

Kapoor

Joshi

2022

International Journal of Applied Mechanics and Engineering

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In the present paper, trigonometric B-spline DQM is applied to get the approximated solution of coupled 2D non-linear Burgers’ equation. This technique, named modified cubic trigonometric B-spline DQM, has been used to obtain accurate and effective numerical approximations of the above-mentioned partial differential equation. For checking the compatibility of results, different types of test examples are discussed. A comparison is done between L2 and L ∞ error norms with the previous, present results and with the exact solution. The resultant set of ODEs has been solved by employing the SSP RK 43 method. It is observed that the obtained results are improved compared to the previous numerical results in the literature.

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“…In 2011, lattice Boltzmann method had been used by Fang Liu and Weiping Shi for solving the system of two-dimensional Burger's equation [ 35 ], while in [ 36 ], the homotopy perturbation method based on the Pade approximation was proposed to solve this system. In 2012, Hossein Aminikhah had introduced a new hybrid of the Laplace transform method and the new homotopy perturbation method (LTNHPM) for solving the system of twodimensional Burger's equation [37]. Mohammad Vaghefi et al in 2014 used finite difference method to solve this system of equations [38].…”

Section: Introductionmentioning

confidence: 99%

Solving Two Dimensional Coupled Burger's Equations and Sine-Gordon Equation Using El-Zaki Transform-Variational Iteration Method

Al-Tai¹,

Al-Fayadh

2021

ANJS

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In this paper, the combined form of the Elzaki transform and variation iteration method is implemented efficiently in finding the analytical and numerical solutions of the two-dimensional nonlinear coupled Burger's partial differential equations and sine-Gordon partial differential equation. The obtained solutions were compared to the exact solutions and other existing methods. Illustrative examples show the efficiency and the power of the used method.

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A New Efficient Method for Solving Two-Dimensional Burgers' Equation

Abstract: We introduce a new hybrid of the Laplace transform method and new homotopy perturbation method (LTNHPM) that efficiently solves nonlinear two-dimensional Burgers' equation. Three examples are given to demonstrate the efficiency of the new method.

Cited by 7 publications

References 13 publications

Solutions of (2+1)-D & (3+1)-D Burgers Equations by New Laplace Variational Iteration Technique

Solutions of (2+1)-D & (3+1)-D Burgers Equations by New Laplace Variational Iteration Technique

A Numerical Approximation of 2D Coupled Burgers’ Equation Using Modified Cubic Trigonometric B-Spline Differential Quadrature Method

Solving Two Dimensional Coupled Burger's Equations and Sine-Gordon Equation Using El-Zaki Transform-Variational Iteration Method

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