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An efficient collocation method based on Hermite formula and cubic B-splines for numerical solution of the Burgers’ equation

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  • Abdullah, Muhammad
  • Yaseen, Muhammad
  • De la Sen, Manuel

Abstract

In this paper, an efficient computational technique for the numerical solution of the Burgers’ equation (BE) is presented. The derivative in space is approximated using cubic B-splines and the Hermite formula whereas time discretization is performed by finite differences. The stability of the proposed scheme is derived using the standard von Neumann method to establish the fact that the errors do not amplify. Convergence analysis for the proposed scheme is also discussed. A sufficiently smooth piecewise continuous function is obtained as an approximation to the exact solution which enables us to approximate the solution at any wanted position in the domain. Numerical tests are carried out to further confirm the accuracy and stability of the method. The outcomes of this study are compared with those previously presented in literature.

Suggested Citation

  • Abdullah, Muhammad & Yaseen, Muhammad & De la Sen, Manuel, 2022. "An efficient collocation method based on Hermite formula and cubic B-splines for numerical solution of the Burgers’ equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 166-184.
    • Handle: RePEc:eee:matcom:v:197:y:2022:i:c:p:166-184
    DOI: 10.1016/j.matcom.2022.02.013
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    References listed on IDEAS

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    1. Idris Dag & Dursun Irk & Ali Sahin, 2005. "B-spline collocation methods for numerical solutions of the Burgers' equation," Mathematical Problems in Engineering, Hindawi, vol. 2005, pages 1-18, January.
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