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Numerical solution of Burgers’ equation by B-spline collocation

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Abstract

In this paper, the Burgers’ equation which is two-dimensional in space, time dependent parabolic differential equation was solved by b-spline collocation algorithms for solving two-dimensional parabolic partial differential equation. At first b-spline interpolation is introduced moreover, the numerical solution is represented as a bi-variate piecewise polynomial with unknown time-dependent coefficients are determined by requiring the numerical solution to satisfy the PDE at a number of points within the spatial domain i.e. we collocate simultaneously in both spatial dimensions. The accuracy of the proposed method is demonstrates by some test problems. The numerical results are found good agreement with exact solution.

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Authors and Affiliations

  1. School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16844-13114, Iran

    M. Yousefi & J. Rashidinia

  2. Energy and Mechanical Engineering Department, Abbaspour-Power and Water, College of Engineering, Shahid Beheshti University, P.O. Box.16765-1719, Tehran, Iran

    M. Yousefi

  3. Institute of Applied Materials-Reliability of Components and Systems (IAM-ZBS), Engelbert-Arnold-Straße, 476131, Karlsruhe, Germany

    M. Moudi

Authors
  1. M. Yousefi
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  2. J. Rashidinia
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  3. M. Yousefi
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  4. M. Moudi
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Correspondence to M. Yousefi.

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Yousefi, M., Rashidinia, J., Yousefi, M. et al. Numerical solution of Burgers’ equation by B-spline collocation. Afr. Mat. 27, 1287–1293 (2016). https://doi.org/10.1007/s13370-016-0409-0

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  • DOI: https://doi.org/10.1007/s13370-016-0409-0

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