An evaluation of multispecies population dynamics models through numerical simulations using the new iterative method

This study explores the multispecies Lotka-Volterra population dynamics models, a captivating nonlinear mathematical framework with significant applications in natural sciences and environmental studies. The primary objective is to deliver precise solutions for these models using the New Iterative Method (NIM). Numerical simulations are conducted on three distinct types of nonlinear dynamic problems, comparing the accuracy of the NIM with that of the Perturbation Iteration Algorithm (PIA), existing exact solutions, and the traditional fourth-order Runge–Kutta method. A continuous step time of Δ = 0.001 was used for the Runge–Kutta method in all computations. Notably, the NIM's solutions for the nonlinear multispecies Lotka-Volterra models demonstrate very good accuracy, achieving convergence to the Runge–Kutta method's solutions within five iterations. The correctness of the NIM is found to be better than the other existing solutions. Its distinctive attribute lies in its computational efficiency, providing high accuracy without necessitating linearization, discretization, multipliers, or polynomials for nonlinear terms. This leads to simpler solution procedures while maintaining commendable accuracy. The findings underscore NIM's reliability and broad applicability in both linear and nonlinear models, highlighting its potential as an invaluable tool in numerical computation.