scholarly journals Bessel collocation approach for solving continuous population models for single and interacting species

2012 ◽  
Vol 36 (8) ◽  
pp. 3787-3802 ◽  
Author(s):  
Şuayip Yüzbaşı
Keyword(s):  
Population Models ◽  
Interacting Species ◽  
Collocation Approach ◽  
Continuous Population

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

2018 ◽  
Vol 11 (08) ◽  
pp. 1850109 ◽  
Author(s):  
M. A. Ramadan ◽  
M. A. Abd El Salam
Keyword(s):  
Collocation Method ◽  
Chebyshev Approximation ◽  
Accurate Method ◽  
Population Models ◽  
Spectral Collocation Method ◽  
Logistic Growth ◽  
Spectral Collocation ◽  
Interacting Species ◽  
Continuous Population ◽  
Predator Model

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.

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