Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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A FOURTH-ORDER ACCURATE FINITE DIFFERENCE SCHEME FOR THE EXTENDED-FISHER-KOLMOGOROV EQUATION

  • Kadri, Tlili (Faculte des Sciences de Tunis Campus Universitaire) ;
  • Omrani, Khaled (Institut Superieur des Sciences Appliquees et de Technologie de Sousse)
  • Received : 2016.12.23
  • Accepted : 2017.06.14
  • Published : 2018.01.31
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Abstract

In this paper, a nonlinear high-order difference scheme is proposed to solve the Extended-Fisher-Kolmogorov equation. The existence, uniqueness of difference solution and priori estimates are obtained. Furthermore, the convergence of the difference scheme is proved by utilizing the energy method to be of fourth-order in space and second-order in time in the discrete $L^{\infty}-norm$. Some numerical examples are given in order to validate the theoretical results.

Keywords

Table 1. The maximum norm errors and spatial convergenceorder with ？xed time step k = 1/10000.

E1BMAX_2018_v55n1_297_t0001.png 이미지

Table 2. The maximum norm errors and temporal conver-gence order with ？xed space step h = 1/500.

E1BMAX_2018_v55n1_297_t0002.png 이미지

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