On the exact and numerical solutions to a nonlinear model arising in mathematical biology

¹ Department of Actuary, Firat University, Elazig, Turkey
² Department of Mathematics, Firat University, Elazig, Turkey
³ Department of Mathematics, Federal University, Dutse, Jigawa, Nigeria
⁴ Department of Computer Engineering, Munzur University, Tunceli, Turkey
⁵ Mugla Sitki Kocman University, Mugla, Turkey

^* Corresponding Author: sibela@mu.edu.tr

Abstract

This study acquires the exact and numerical approximations of a reaction-convection-diffusion equation arising in mathematical bi- ology namely; Murry equation through its analytical solutions obtained by using a mathematical approach; the modified exp(-Ψ(η))-expansion function method. We successfully obtained the kink-type and singular soliton solutions with the hyperbolic function structure to this equa- tion. We performed the numerical simulations (3D and 2D) of the obtained analytical solutions under suitable values of parameters. We obtained the approximate numerical and exact solutions to this equa- tion by utilizing the finite forward difference scheme by taking one of the obtained analytical solutions into consideration. We investigate the stability of the finite forward difference method with the equation through the Fourier-Von Neumann analysis. We present the L₂ and L_∞ error norms of the approximations. The numerical and exact approx- imations are compared and the comparison is supported by a graphic plot. All the computations and the graphics plots in this study are car- ried out with help of the Matlab and Wolfram Mathematica softwares. Finally, we submit a comprehensive conclusion to this study.