Spectral collocation method for solving continuous population models for single and interacting species by means of exponential Chebyshev approximation

Abstract

In this paper, an efficient and accurate method is presented to solve continuous population models for single and interacting species using spectral collocation method with exponential Chebyshev (EC) functions. The first problem is a logistic growth model in a population, while the second problem is a prey–predator model: Lotka–Volterra system, the third is a simple 2-species Lotka–Volterra competition model, and the final one is a prey–predator model with limit cycle periodic behavior. The high accuracy of this method is verified through some numerical examples. The obtained numerical results are compared with other methods, showing that the proposed method gives higher accuracy.