Comparative analysis of Lotka-Volterra type models with numerical methods using residuals in Mathematica

Abstract

This paper details the approximate solution to the Lotka-Volterra type models with no closed-form by employing the use of two numerical techniques; Runge-Kutta Fehlberg and the 4-stage Runge-Kutta method. From the numerical techniques used, a comparative analysis is carried out, and an approximate solution is obtained. Two cases were considered, case 1 details on indistinguishable graphs but different numerical values (not enough to conclude on the efficient technique) are obtained using the two techniques and while case 2 shows that both numerical techniques give same graphical representation and numerical values, hence this necessitate the reason for this investigation; by so doing the log-plots and residuals was introduced to obtain the most effective and efficient technique under such condition.