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

P. Danumjaya & A. K. Pani

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

Published online: 2006-03

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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.

  • Keywords

extended Fisher-Kolmogorov (EFK) equation, Lyapunov functional, weak solution, existence, uniqueness and regularity results, finite element method, semidiscrete method, backward Euler, two step backward difference and Crank-Nicolson schemes, optimal estimates.

  • AMS Subject Headings

65L20, 65L60, 65L70

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-3-186, author = {P. Danumjaya and A. K. Pani}, title = {Numerical Methods for the Extended Fisher-Kolmogorov (EFK) Equation}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2006}, volume = {3}, number = {2}, pages = {186--210}, 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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/896.html} }
TY - JOUR T1 - Numerical Methods for the Extended Fisher-Kolmogorov (EFK) Equation AU - P. Danumjaya & A. K. Pani JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 186 EP - 210 PY - 2006 DA - 2006/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/896.html KW - extended Fisher-Kolmogorov (EFK) equation, Lyapunov functional, weak solution, existence, uniqueness and regularity results, finite element method, semidiscrete method, backward Euler, two step backward difference and Crank-Nicolson schemes, optimal estimates. AB -

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.

P. Danumjaya and A. K. Pani. (2006). Numerical Methods for the Extended Fisher-Kolmogorov (EFK) Equation. International Journal of Numerical Analysis and Modeling. 3 (2). 186-210. doi:
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