10.1007/s40096-021-00410-8

Nonlinear dynamics of the Burgers’ equation and numerical experiments

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  • Ali Başhan*1,
  1. Department of Mathematics, Faculty of Science and Art, Zonguldak Bulent Ecevit University, Zonguldak, 67100, TR

Published in Issue 2021-05-09

How to Cite

Başhan, A. (2021). Nonlinear dynamics of the Burgers’ equation and numerical experiments. Mathematical Sciences, 16(2 (June 2022). https://doi.org/10.1007/s40096-021-00410-8
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Abstract

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.

Keywords

  • Burgers’ equation,
  • Convergence,
  • Modified quintic B-spline,
  • Differential quadrature method,
  • Finite difference method

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