A Galerkin-like approach to solve continuous population models for single and interacting species
Keywords:
Continuous population models, Galerkin method, logistic equation, predator-prey equation, residual error correction.Abstract
In this paper, we present a Galerkin-like approach to numerically solve continuous population models for single and interacting species. After taking inner product of a set of monomials with a vector obtained from the problem under consideration, the problem is transformed to a nonlinear system of algebraic equations. The solution of this system gives the coefficients of the approximate solutions. Additionally, the technique of residual correction, which aims to increase the accuracy of the approximate solution by estimating its error, is discussed in some detail. The method and the residual correction technique areillustrated with two examples. The results are also compared with numerous existing methods from the literature.
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