Numerical investigation of nonlinear extended Fisher-Kolmogorov equation via quintic trigonometric B-spline collocation technique

Shafeeq Rahman Thottoli; Mohammad Tamsir; Mutum Zico Meetei; Ahmed H. Msmali; Shafeeq Rahman Thottoli; Mohammad Tamsir; Mutum Zico Meetei; Ahmed H. Msmali

doi:10.3934/math.2024843

AIMS Mathematics

2024, Volume 9, Issue 7: 17339-17358. doi: 10.3934/math.2024843

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Research article

Numerical investigation of nonlinear extended Fisher-Kolmogorov equation via quintic trigonometric B-spline collocation technique

1.
Department of Physical Sciences, Physics Division, College of Science, Jazan University, P.O. Box 114, Jazan 45142, Kingdom of Saudi Arabia
2.
Department of Mathematics, College of Science, Jazan University, P.O. Box 114, Jazan 45142, Kingdom of Saudi Arabia
3.
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522, Australia

Received: 05 February 2024 Revised: 19 April 2024 Accepted: 26 April 2024 Published: 20 May 2024
MSC : 35-XX, 65-XX, 74S30

In this article, a collocation technique based on quintic trigonometric B-spline (QTB-spline) functions was presented for homogeneous as well as the nonhomogeneous extended Fisher-Kolmogorov (F-K) equation. This technique was used for space integration, while the time-derivative was discretized by the usual finite difference method (FDM). To handle the nonlinear term, the process of Rubin-Graves (R-G) type linearization was employed. Three examples of the homogeneous extended F-K equation and one example of the nonhomogeneous extended F-K equation were considered for the analysis. Stability analysis and numerical convergence were also discussed. It was found that the discretized system of the extended F-K equation was unconditionally stable, and the projected technique was second order accurate in space. The consequences were portrayed graphically to verify the accuracy of the outcomes and performance of the projected technique, and a relative investigation was accomplished graphically. The figured results were found to be extremely similar to the existing results.
- homogeneous and nonhomogeneous extended F-K equation,
- collocation technique,
- QTB-spline functions,
- R-G type linearization process,
- stability analysis,
- convergence
Citation: Shafeeq Rahman Thottoli, Mohammad Tamsir, Mutum Zico Meetei, Ahmed H. Msmali. Numerical investigation of nonlinear extended Fisher-Kolmogorov equation via quintic trigonometric B-spline collocation technique[J]. AIMS Mathematics, 2024, 9(7): 17339-17358. doi: 10.3934/math.2024843

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Abstract

In this article, a collocation technique based on quintic trigonometric B-spline (QTB-spline) functions was presented for homogeneous as well as the nonhomogeneous extended Fisher-Kolmogorov (F-K) equation. This technique was used for space integration, while the time-derivative was discretized by the usual finite difference method (FDM). To handle the nonlinear term, the process of Rubin-Graves (R-G) type linearization was employed. Three examples of the homogeneous extended F-K equation and one example of the nonhomogeneous extended F-K equation were considered for the analysis. Stability analysis and numerical convergence were also discussed. It was found that the discretized system of the extended F-K equation was unconditionally stable, and the projected technique was second order accurate in space. The consequences were portrayed graphically to verify the accuracy of the outcomes and performance of the projected technique, and a relative investigation was accomplished graphically. The figured results were found to be extremely similar to the existing results.

References

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