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Bull. Korean Math. Soc. 2018; 55(1): 297-310
Online first article September 12, 2017 Printed January 31, 2018
https://doi.org/10.4134/BKMS.b161013
Copyright © The Korean Mathematical Society.
A fourth-order accurate finite difference scheme for the extended-Fisher-Kolmogorov equation
Tlili Kadri, Khaled Omrani
Campus Universitaire, Institut Sup\'erieur des Sciences Appliqu\'ees et de Technologie de Sousse
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
MSC numbers: 65M06, 65M12, 65M15
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