Abstract
The analytical and numerical solutions of the (2+1) dimensional, Fisher-Kolmogorov-Petrovskii-Piskunov ((2+1) D-Fisher-KPP) model are investigated by employing the modified direct algebraic (MDA), modified Kudryashov (MKud.), and trigonometric-quantic B-spline (TQBS) schemes. This model, which arises in population genetics and nematic liquid crystals, describes the reaction–diffusion system by traveling waves in population genetics and the propagation of domain walls, pattern formation in bi-stable systems, and nematic liquid crystals. Many novel analytical solutions are constructed. These solutions are used to evaluate the requested numerical technique’s conditions. The numerical solutions of the considered model are studied, and the absolute value of error between analytical and numerical is calculated to demonstrate the matching between both solutions. Some figures are represented to explain the obtained analytical solutions and the match between analytical and numerical results. The used schemes’ performance shows their effectiveness and power and their ability to handle many nonlinear evolution equations.
Highlights
In the last century, and especially in the biological system, diffusion has been employed as one of the most famous models for spatial spread
Especially in the biological system, diffusion has been employed as one of the most famous models for spatial spread. It has been used for several services, such as invasion and pattern formation, ecology, motile cell populations, wound healing, the capillary growth network, the spatial movement of cell populations, and so on [1,2,3,4,5]
For studying closely packed cells such as epithelium [6], the linear diffusion model is not considered as an excellent idea where it contains a movement cell population; that is why the reaction–diffusion equation is a perfect bi-mathematical model [7]
Summary
Especially in the biological system, diffusion has been employed as one of the most famous models for spatial spread. This paper employs three recent analytical and numerical techniques [34,35,36,37,38] to investigate novel analytical wave solutions of Equation (3)’s accuracy of the used analytical schemes. The other sections in this paper are given in the following order; Section 2 shows the novel and accurate solutions of the considered model through the above-mentioned analytical and numerical schemes. + l1 where li , i = 1, 2, 3 are arbitrary constants to be determined later, to Equation (4), we obtain the following sets of the above-mentioned parameters: Set I q. Where k is an arbitrary constant to be determined later, to Equation (4), we obtain the following sets of the above-mentioned parameters: a0 = −1, a1 = 2, r = 2, μ = −.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
