A fourth-order accurate finite difference scheme for the extended-Fisher-Kolmogorov equation
Bull. Korean Math. Soc. 2018 Vol. 55, No. 1, 297-310
https://doi.org/10.4134/BKMS.b161013
Published online January 31, 2018
Tlili Kadri, Khaled Omrani
Campus Universitaire, Institut Sup\'erieur des Sciences Appliqu\'ees et de Technologie de Sousse
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
MSC numbers : 65M06, 65M12, 65M15
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