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http://dx.doi.org/10.4134/BKMS.b161013

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)
Publication Information
Bulletin of the Korean Mathematical Society / v.55, no.1, 2018 , pp. 297-310 More about this Journal
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
extended Fisher-Kolmogorov equation; difference scheme; existence; uniqueness; high-order convergence;
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