Haar wavelet-based numerical investigation of coupled viscous Burgers' equation

Mittal, R. C.; Kaur, Harpreet; Mishra, Vinod

doi:10.1080/00207160.2014.957688

Cited by 17 publications

(13 citation statements)

References 22 publications

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“…Lastly we consider the coupled Burgers' equation (1.1), (1.2) for α = β = 1 and η = ξ = −2 so that equations (1.1), (1.2) take the following form: Table 4. The obtained results by the present method are in good agreement with Haar wavelet method [29] and are better than Finite element method [23]. The physical behavior of numerical solutions for α = β = 1 and η = ξ = −2 between t = 0 and t = 2 and for α = 3, β = 2 and η = 1, ξ = −2 between t = 0 and t = 1.5 are depicted with contour forms in Fig.…”

Section: Problemsupporting

confidence: 73%

“…. In the studies [22,29], coupled Burgers' equations are solved by Haar wavelet method. Rashid et al have solved the coupled viscous Burgers' equation by Chebyshev-Legendre Pseudo-Spectral method in [33].…”

Section: Introductionmentioning

confidence: 99%

“…Due to these facts, researchers have focused on more simple wavelets such as Haar wavelets, Legendre wavelets and Chebyshev wavelets for obtaining numerical solutions of differential and integral equations. There are a lot of studies on application of Haar wavelets in solving differential and integral equations numerically [6,7,9,18,22,24,26,27,29,31,32,40]. Nowadays, Legendre and Chebyshev wavelets are studied by many researchers [3,4,8,13,14,35,36,38,39,[44][45][46][47].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Chebyshev Wavelet Method for Numerical Solutions of Coupled Burgers Equation

Oruç¹,

Bulut²,

Esen³

2018

HJMS

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This paper deals with the numerical solutions of one dimensional time dependent coupled Burgers' equation with suitable initial and boundary conditions by using Chebyshev wavelets in collaboration with a collocation method. The proposed method converts coupled Burgers' equations into system of algebraic equations by aid of the Chebyshev wavelets and their integrals which can be solved easily with a solver. Benchmarking of the proposed method with exact solution and other known methods already exist in the literature is made by three test problems. The feasibility of the proposed method is demonstrated by test problems and indicates that the proposed method gives accurate results in short cpu times. Computer simulations show that the proposed method is computationally cheap, fast and quite good even in the case of less number of collocation points.

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Section: Problemsupporting

confidence: 73%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Chebyshev Wavelet Method for Numerical Solutions of Coupled Burgers Equation

Oruç¹,

Bulut²,

Esen³

2018

HJMS

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“…Results of the problem are reported in Table XIII. In Table XIII, compared L ∞ and RMS errors of LRBF-DQM and GRBF-DQM for a0=0.05, A=a02(4αβ−12α−1) and it is concluded that LRBF-DQM algorithm is better than GRBF-DQM and other schemes proposed in Mittal et al (2015) and Rashid and Ismail (2009).…”

Section: Numerical Experiments and Discussionmentioning

confidence: 97%

Meshfree algorithms based on radial basis functions for numerical simulation and to capture shocks behavior of Burgers’ type problems

Jiwari

Kumar

Mittal

2019

Self Cite

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Purpose The purpose of this paper is to develop two meshfree algorithms based on multiquadric radial basis functions (RBFs) and differential quadrature (DQ) technique for numerical simulation and to capture the shocks behavior of Burgers’ type problems. Design/methodology/approach The algorithms convert the problems into a system of ordinary differential equations which are solved by the Runge–Kutta method. Findings Two meshfree algorithms are developed and their stability is discussed. Numerical experiment is done to check the efficiency of the algorithms, and some shock behaviors of the problems are presented. The proposed algorithms are found to be accurate, simple and fast. Originality/value The present algorithms LRBF-DQM and GRBF-DQM are based on radial basis functions, which are new for Burgers’ type problems. It is concluded from the numerical experiments that LRBF-DQM is better than GRBF-DQM. The algorithms give better results than available literature.

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“…After this achievement researchers have been using Haar wavelets to obtain numerical solutions of differential equations because of their simplicity and computational features. Recently, many authors have used Haar wavelet method for solving ordinary and partial differential equations [20][21][22][23][24][25][26][27][28][29][30][31]. Especially high order pdes like KdV and fractional coupled KdV equations are considered in [32,33].…”

Section: Haar Waveletsmentioning

confidence: 99%

A numerical treatment based on Haar wavelets for coupled KdV equation

Oruç¹,

Bulut

Esen

2017

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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In this paper, numerical solutions of one dimensional coupled KdV equation has been investigated by Haar Wavelet method. Time derivatives given in this equation are discretized by finite differences and nonlinear terms appearing in the equations are linearized by some linearization techniques and space derivatives are discretized by Haar wavelets. For examining performance of the proposed method, single soliton solution and conserved quantities of some test problems are used. Also error analysis of numerical scheme is investigated and numerical results are compared with some results already existing in the literature.

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Haar wavelet-based numerical investigation of coupled viscous Burgers' equation

Cited by 17 publications

References 22 publications

Chebyshev Wavelet Method for Numerical Solutions of Coupled Burgers Equation

Chebyshev Wavelet Method for Numerical Solutions of Coupled Burgers Equation

Meshfree algorithms based on radial basis functions for numerical simulation and to capture shocks behavior of Burgers’ type problems

A numerical treatment based on Haar wavelets for coupled KdV equation

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