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A differential quadrature based numerical method for highly accurate solutions of Burgers' equation
Author(s) -
Aswin V. S.,
Awasthi Ashish,
Rashidi Mohammad Mehdi
Publication year - 2017
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22178
Subject(s) - burgers' equation , mathematics , discretization , quadrature (astronomy) , nyström method , nonlinear system , partial differential equation , simple (philosophy) , grid , polynomial , computation , mathematical analysis , algorithm , integral equation , philosophy , physics , geometry , electrical engineering , epistemology , quantum mechanics , engineering
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