Combination of nonstandard schemes and Richardson’s extrapolation to improve the numerical solution of population models

In this paper we combine nonstandard finite-difference ( N S F D ) schemes and Richardson’s extrapolation method to obtain numerical solutions of two biological systems. The first biological system deals with the dynamics of phytoplankton–nutrient interaction under nutrient recycling and the second one deals with the modeling of whooping cough in the human population. Since both models requires positive solutions, the numerical solutions need to satisfy this property. In addition, it is necessary in some cases that numerical solutions reproduce correctly the dynamical behavior while in other cases it is necessary just to find the steady state. N S F D schemes can do this. In this paper Richardson’s extrapolation is applied directly to the N S F D solution to increase the order of accuracy of the numerical solutions of these biological systems. Numerical results show that Richardson’s extrapolation method improves accuracy.