A node-moving algorithm with application to Burgers equation and the Moltz problem

Cook, Andy; Duncan, R.

doi:10.1016/s0307-904x(82)80008-5

Cited by 5 publications

(2 citation statements)

References 3 publications

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“…Substitute the derivative approximations, Eqs. (12) and (13) in linearized Burgers' equation, Eq. (4) leads to the discretized Burgers' equation Eq.…”

Section: Step 2: Discretizationmentioning

confidence: 99%

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A differential quadrature based numerical method for highly accurate solutions of Burgers' equation

Aswin

Awasthi

Rashidi

2017

Numerical Methods Partial

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In this article, we introduce a new, simple, and accurate computational technique for one‐dimensional Burgers' equation. The idea behind this method is the use of polynomial based differential quadrature (PDQ) for the discretization of both time and space derivatives. The quasilinearization process is used for the elimination of nonlinearity. The resultant scheme has simulated for five classic examples of Burgers' equation. The simulation outcomes are validated through comparison with exact and secondary data in the literature for small and large values of kinematic viscosity. The article has deduced that the proposed scheme gives very accurate results even with less number of grid points. The scheme is found to be very simple to implement. Hence, it applies to any domain requires quick implementation and computation.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 2023–2042, 2017

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“…Substitute the derivative approximations, Eqs. (12) and (13) in linearized Burgers' equation, Eq. (4) leads to the discretized Burgers' equation Eq.…”

Section: Step 2: Discretizationmentioning

confidence: 99%

“…Morandi et al conducted the stability and error estimate of the numerical method proposed by Varoglu. Further, finite elements methods for Burgers' equation are described in . Bressan and Quarteroni used Chebyshev spectral collocation methods for solving viscid Burgers' equation.…”

Section: Introductionmentioning

confidence: 99%