The behavior of population dispersion employing various numerical techniques

Abstract

The exploration of population diversity motivated us to present this paper. A mathematical model for the ecological process of population dispersion is finally considered by us to figure out the dispersion of population along the area. The dispersal from one's home site to the next is considered the most important phenomenon in the demographic and evolutionary dynamics of the population. The most important factor regarding dispersal is the spatial distribution of individuals. This dispersal may result in enhanced clamping, huge randomness, or even more spacing. The Adomian Decomposition method has opted to work out the problem analytically. Numerical schemes brought an approximate solution by incorporating the Forward-in-Time and Central-In-Space (FTCS) scheme, the Crank Nicolson (CN) scheme, and Numerov’s method. The validity and efficiency of schemes employed for the proposed model are supported by core properties like stability, consistency, and convergence. A comparison is made between the results calculated via schemes and the one analytically.