A novel numerical scheme for solving Burgers’ equation

Xu, Min; Wang, Ren-Hong; Zhang, Jihong; Fang, Qin

doi:10.1016/j.amc.2010.10.050

Cited by 45 publications

(32 citation statements)

References 31 publications

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“…Error analysis comparison of results at t = 0.1 for  = 1, Δt = 0.00001, h = 0.0125 is shown in Table 2. A comparison of present method is shown in Table 3, with previous ones reported by [14,15]. In Figure 3, the error analysis comparison of results at t = 0.1 for  = 1, Δt = 0.00001, h = 0.0125 has presented.…”

Section: Discretization Using Approximating Functionmentioning

confidence: 94%

“…In particular, for The theoretical solution of this problem was expressed as an infinite series by Cole [5]. For different viscosity parameters, a comparison of results for present work with the previous work [12,13,14,15] at t = 0.1 for ν = 1, Δt = 0.00001, h = 0.0125, are presented in Table 1. Error analysis comparison of results at t = 0.1 for  = 1, Δt = 0.00001, h = 0.0125 is shown in Table 2.…”

Section: Discretization Using Approximating Functionmentioning

confidence: 99%

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Solution of Burger’s Equations by Orthogonal Collocation on Finite Elements Hermite Basis

2016

6th International Conference on Advances in Engineering Sciences and Applied Mathematics (ICAESAM-2016) Dec. 21-22, 2016 Kuala

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Abstract-Nonlinear parabolic Burgers' equations arising in unsteady flow of the generalized Newtonian fluid are solved numerically by Orthogonal Collocation on Finite Elements using Hermite Basis. The technique is used for discretization along with the zeros of Chebyshev polynomial as collocation points. Results are compared with exact solution and error analysis is shown for different techniques used earlier for the solution of the Burger's equations.

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Section: Discretization Using Approximating Functionmentioning

confidence: 94%

Section: Discretization Using Approximating Functionmentioning

confidence: 99%

Solution of Burger’s Equations by Orthogonal Collocation on Finite Elements Hermite Basis

2016

6th International Conference on Advances in Engineering Sciences and Applied Mathematics (ICAESAM-2016) Dec. 21-22, 2016 Kuala

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“…These aims will be done by comparing ECEM to other numerical approaches based on the finite difference method [16,23], finite element method [28], cubic spline and sinc-function methods [31,32], and the fourth-order Runge-Kutta method [21] (RK4) and the BDF-type Chebyshev approximation based fourth-order implicit Runge-Kutta method [29] (CCM). The numerical errors are measured by the following maximum and l 2 norms…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…Table 8 explains both advantage and disadvantage about ECEM with the modified B-spline approximation and the pseudo-spectral approximation for the spatial discretization. For the B-spline approximation (BS), the required cpu time to get the similar maximum error for three time discretizations, Euler method ( [32]), RK4 and ECEM are measured at different times. Even if ECEM and RK4 are fourth order convergence in time, ECEM allows much larger time step τ = 0.04 than τ = 0.005 while RK4+BS spends less cpu time than ECEM+BS does for the same accuracy under ϵ = 0.001 and M = 79.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…For example, one may refer to the approaches based on the finite difference method ( [2,12,16,18,20,23,27]), Galerkin method ( [11,17,33]), finite element method ( [1,8,10,19,24,28]), spectral method ( [4,6,26]) and cubic spline and sinc-function methods ( [1,24,31,32] etc. Most of the mentioned numerical approaches are using various computational techniques in spatial discretizations to get more accurate approximations.…”

Section: Introductionmentioning

confidence: 99%

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A New Time Stepping Method for Solving One Dimensional Burgers' Equations

Piao¹,

Kim²,

Kim³

et al. 2012

Kyungpook mathematical journal

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Abstract. In this paper, we present a simple explicit type numerical method for discretizations in time for solving one dimensional Burgers' equations. The proposed method does not need an iteration process that may be required in most implicit methods and have good convergence and efficiency in computational sense compared to other known numerical methods. For evidences, several numerical demonstrations are also provided.

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Study of dynamical behavior of Burgers' equation in quantum modeling

Gupta

Shukla

Singh

2023

Math Methods in App Sciences

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Our main goal is to investigate the dynamical behavior of the quantum model of Bateman–Burgers equation utilizing a new hybrid semidiscretization technique: nCB‐DQT‐RK scheme. The nCB‐DQT‐RK is traditional differential quadrature technique (DQT) with newly modified cubic B‐splines (nCB), as a basis, which have been utilized for the discretization of spatial derivatives, and the time integration scheme SSP‐RK for the temporal discretization. The efficiency/effectiveness of the reported nCB‐DQT‐RK results, computationally, are illustrated not only numerically but also graphically for better cognizance and reliable performance of the nCB‐DQT‐RK. This is validated based on the estimation of evaluated accuracy by means of stability and convergence analysis, which infer that the proposed nCB‐DQT‐RK scheme is capable of producing stable results with spatial convergence of order four, and the use of nCB in DQT is capable to improve performance (in terms of accuracy and spatial rate of convergence as well) as compared to existing techniques (collocation/quadrature) with traditional cubic B‐splines and its existing modifications, and so, nCB is capable to surpass cubic B‐splines and its existing modification.

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A novel numerical scheme for solving Burgers’ equation

Cited by 45 publications

References 31 publications

Solution of Burger’s Equations by Orthogonal Collocation on Finite Elements Hermite Basis

Solution of Burger’s Equations by Orthogonal Collocation on Finite Elements Hermite Basis

A New Time Stepping Method for Solving One Dimensional Burgers' Equations

Study of dynamical behavior of Burgers' equation in quantum modeling

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