Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
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A HIGHER ORDER NUMERICAL SCHEME FOR SINGULARLY PERTURBED BURGER-HUXLEY EQUATION

  • Jiwrai, Ram (Department of Mathematics, Indian Institute of Technology Roorkee) ;
  • Mittal, R.C. (Department of Mathematics, Indian Institute of Technology Roorkee)
  • 투고 : 2010.04.13
  • 심사 : 2010.08.16
  • 발행 : 2011.05.30
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초록

In this article, we present a numerical scheme for solving singularly perturbed (i.e. highest -order derivative term multiplied by small parameter) Burgers-Huxley equation with appropriate initial and boundary conditions. Most of the traditional methods fail to capture the effect of layer behavior when small parameter tends to zero. The presence of perturbation parameter and nonlinearity in the problem leads to severe difficulties in the solution approximation. To overcome such difficulties the present numerical scheme is constructed. In construction of the numerical scheme, the first step is the dicretization of the time variable using forward difference formula with constant step length. Then, the resulting non linear singularly perturbed semidiscrete problem is linearized using quasi-linearization process. Finally, differential quadrature method is used for space discretization. The error estimate and convergence of the numerical scheme is discussed. A set of numerical experiment is carried out in support of the developed scheme.

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피인용 문헌

  1. A new algorithm based on modified trigonometric cubic B-splines functions for nonlinear Burgers’-type equations vol.27, pp.8, 2017, https://doi.org/10.1108/hff-05-2016-0191
  2. Numerical Study of the Inverse Problem of Generalized Burgers-Fisher and Generalized Burgers-Huxley Equations vol.2021, pp.None, 2011, https://doi.org/10.1155/2021/6652108