Volume 3, Issue 2
Numerical Methods for the Extended Fisher-Kolmogorov (EFK) Equation

P. Danumjaya and A. K. Pani

Int. J. Numer. Anal. Mod., 3 (2006), pp. 186-210

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  • Abstract

In the study of pattern formation in bi-stable systems, the extended Fisher-Kolmogorov (EFK) equation plays an important role. In this paper, some a priori bounds are proved using Lyapunov functional. Further, existence, uniqueness and regularity results for the weak solutions are derived. Using C-1-conforming finite element method, optimal error estimates are established for the semidiscrete case. Finally, fully discrete schemes like backward Euler, two step backward difference and Crank-Nicolson methods are proposed, related optimal error estimates are derived and some computational experiments are discussed.

  • History

Published online: 2006-03

  • AMS Subject Headings

65L20, 65L60, 65L70

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