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Hybrid B-Spline Collocation Method for Solving the Generalized Burgers-Fisher and Burgers-Huxley Equations

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  • Imtiaz Wasim
  • Muhammad Abbas
  • Muhammad Amin

Abstract

In this study, we introduce a new numerical technique for solving nonlinear generalized Burgers-Fisher and Burgers-Huxley equations using hybrid B-spline collocation method. This technique is based on usual finite difference scheme and Crank-Nicolson method which are used to discretize the time derivative and spatial derivatives, respectively. Furthermore, hybrid B-spline function is utilized as interpolating functions in spatial dimension. The scheme is verified unconditionally stable using the Von Neumann (Fourier) method. Several test problems are considered to check the accuracy of the proposed scheme. The numerical results are in good agreement with known exact solutions and the existing schemes in literature.

Suggested Citation

  • Imtiaz Wasim & Muhammad Abbas & Muhammad Amin, 2018. "Hybrid B-Spline Collocation Method for Solving the Generalized Burgers-Fisher and Burgers-Huxley Equations," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-18, January.
    • Handle: RePEc:hin:jnlmpe:6143934
    DOI: 10.1155/2018/6143934
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