Computational and numerical simulations for the nonlinear fractional Kolmogorov-Petrovskii-Piskunov (FKPP) equation

摘要

This research paper elucidates solitary, compacton, and peakon computational solutions, and numerical solutions of the nonlinear fractional Kolmogorov-Petrovskii-Piskunov (FKPP) equation that belongs to the class of reaction-diffusion equation. This equation describes the behavior of genetic models in the increase of microorganisms. Usually, it is used as a biological model to investigate the microbiological densities in bacteria cells as a result of diffusion mechanisms in terms of space-time. The present framework depends on applying the modified Khater method to the FKPP equation to extract the computational solutions then using these solutions to get necessary boundary conditions to implement the numerical B-spline schemes on the suggested equation. The reliability and accuracy of the computational method and solutions are verified by using numerical simulations. For more explanation of the obtained analytical solutions, some sketches are plotted in different types. Also, the comparison between the distinct types of obtained solutions is shown by calculating the absolute value of error.