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Nonlinear dynamics of the Burgers’ equation and numerical experiments

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A Correction to this article was published on 12 June 2021

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Abstract

In this study, we have modified quintic B-spline base function to use for numerical solution of the Burgers’ equation. For this purpose, the numerical algorithm differential quadrature method and Crank–Nicolson scheme are used for space and time discretization, respectively. To deal with nonlinear terms, they are linearized by using Rubin–Graves technique. To observe the accuracy of the present modification, ten different and important test problems are solved successfully. The present results are compared with earlier single methods and mixed methods to see the efficiency of the present algorithm. All comparisons display that the present approach developed the numerical results according to earlier ones. Numerical simulations are plotted at selected time steps to observe the physical behaviour of the waves in 2D and 3D. The rate of convergence related to space is calculated for different examples and reported with error norms.

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  1. Department of Mathematics, Faculty of Science and Art, Zonguldak Bulent Ecevit University, 67100, Zonguldak, Turkey

    Ali Başhan

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Başhan, A. Nonlinear dynamics of the Burgers’ equation and numerical experiments. Math Sci 16, 183–205 (2022). https://doi.org/10.1007/s40096-021-00410-8

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