A differential quadrature based numerical method for highly accurate solutions of Burgers' equation. Issue 6 (3rd July 2017)

• Record Type: Journal Article
• Authors: Aswin, V. S.; Awasthi, Ashish; Rashidi, Mohammad Mehdi
• Is Part Of: Numerical methods for partial differential equations. Volume 33:Issue 6(2017:Nov.)
• Page Start: 2023
• Page End: 2042
• Publication Date: 2017-07-03
• Subjects: Burgers'equation -- polynomial based differential quadrature method -- Chebyshev‐Gauss‐Lobatto grid -- quasilinearization -- highly accurate numerical scheme; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22178
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract : 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