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Original Article

An exponentially fitted numerical technique for singularly perturbed Burgers-Fisher equation on a layer adapted mesh

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Pages 1502-1513 | Received 21 Mar 2018, Accepted 21 Aug 2018, Published online: 19 Sep 2018

References

  • R.E. Bellman and R.E. Kalaba, Quasilinearization and Nonlinear Boundary-Value problems, American Elsevier Publishing, New York, 1965.
  • J. Donea, A Taylor-Galerkin method for convective transport problems, Internat. J. Numer. Methods Engrg. 20 (1984), pp. 101–119. (doi:10.1002/nme.1620200108)
  • J. Donea, L. Quartapelle, and V. Selim, An analysis of time discretization in the finite element solution of hyperbolic problems, J. Comput. Phys. 70 (1987), pp. 463–499. (doi.org/10.1016/0021-9991(87)90191-4)
  • V. Gupta and M.K. Kadalbajoo, Numerical approximation of modified Burger's equation via hybrid finite difference scheme on layer adaptive mesh, Neural Parallel Sci. Comput. 18 (2010), pp. 167–194.
  • M. Javidi, Spectral collocation method for the solution of the generalized Burger-Fisher equation, Appl. Math. Comput. 174 (2006), pp. 345–352. (doi.org/10.1016/j.amc.2005.04.084)
  • J.J.H. Miller, E. O'Riordan, and G.I. Shishkin, Fitted Numerical Methods for Singular Perturbation Problems, World Scientific, Singapore, 1996.
  • R.C. Mittal and A. Tripathi, Numerical solutions of generalized Burgers-Fisher and generalized Burgers-Huxley equations using collocation of cubic B-splines, Int. J. Comput. Math. 92 (2015), pp. 1053–1077. (doi.org/10.1080/00207160.2014.920834)
  • R. Mohammadi, Spline solution of the generalized Burger's-Fisher equation, Appl. Anal. 91 (2012), pp. 2189–2215. (doi.org/10.1080/00036811.2011.596479)
  • H.G. Ross, M. Stynes, and L. Tobiska, Numerical Methods for Singularly Perturbed Differential Problems, Springer, Berlin, 1996.
  • H.G. Roos, M. Stynes, and L. Tobiska, Robust Numerical Methods for Singularly Perturbed Differential Equations, Springer, Berlin, 2008.
  • M. Sari, Differential quadrature solutions of the generalized Burgers-Fisher equation with a strong stability preserving high-order time integration, Math. Comput. Appl. 16 (2011), pp. 477–486.
  • M. Sari, G. Gurarslan, and I. Dag, A compact finite difference method for the solution of the generalized Burger-Fisher equation, Numer. Methods Partial Differential Equations 26 (2010), pp. 125–134. (doi:10.1002/num.20421)
  • R.P. Zhang and L.W. Zhang, Direct discontinuous Galerkin method for the generalized Burgers-Fisher equation, Chin. Phys. B. 21 (2012), pp. 1–4. (doi:10.1088/1674-1056/21/9/090206)
  • R.P. Zhang, X.J. Yu, and G.Z. Zhao, The local discontinuous Galerkin method for Burger's-Huxley and Burger's-Fisher equations, Appl. Math. Comput. 218 (2012), pp. 8773–8778. (doi.org/10.1016/j.amc.2012.02.035)
  • C.G. Zhu and W.S. Kang, Numerical solution of Burgers-Fisher equation by cubic B-spline quasi-interpolation, Appl. Math. Comput. 216 (2010), pp. 2679–2686. (doi.org/10.1016/j.amc.2010.03.113)

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