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A computational method for nonlinear Burgers’ equation using quartic-trigonometric tension B-splines

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Abstract

This work proposes a finite element method emphasizing with quartic-trigonometric basis functions for finding the numerical solution of nonlinear Burgers’ equation. The computational scheme is constructed by a discretized space-time hybrid approach using B-spline functions. This methodology produces a system of time-dependent differential equations which is integrated by finite elements technique. The experimental cases including graphical patterns of each wave interaction are simulated by the current computational algorithm. In addition, the method establishes the capacity to provide highly efficient solutions with relative ease of computation. Investigation of the stability analysis shows that the current computational method serves an unconditional stable numerical scheme.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey

    Gulsemay Yigit

  2. Department of Mathematics and Computer Science, Eskisehir Osmangazi University, Eskisehir, Turkey

    Ozlem Ersoy Hepson

  3. Department of Mathematics, Istinye University, Istanbul, Turkey

    Tofigh Allahviranloo

Authors
  1. Gulsemay Yigit
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  2. Ozlem Ersoy Hepson
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  3. Tofigh Allahviranloo
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Correspondence to Tofigh Allahviranloo.

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Yigit, G., Hepson, O.E. & Allahviranloo, T. A computational method for nonlinear Burgers’ equation using quartic-trigonometric tension B-splines. Math Sci 18, 17–28 (2024). https://doi.org/10.1007/s40096-022-00481-1

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