Rational pseudospectral approximation to the solution of a nonlinear integro-differential equation arising in modeling of the population growth

Pseudospectral approach based on rational Legendre and rational Chebyshev functions is developed to solve the nonlinear integro-differential Volterra’s population model. The model includes an integral term that characterizes accumulated toxicity on the species in addition to the terms of the logistic equation. Since the equation is defined on positive real line, the rational Legendre and the rational Chebyshev functions are used to approximate the unknown function. The approach reduces the solution of the main problem to the solution of a system of nonlinear algebraic equations. The obtained results represent the exponential convergence of the new method, so it can be applied on a wide variety of problems.