Numerical approximations for population growth model by Rational Chebyshev and Hermite Functions collocation approach: A comparison
For researchers solving nonlinear integro-differential equations, this is an incremental comparison of two numerical methods without demonstrating clear superiority.
The paper compares rational Chebyshev and Hermite functions collocation methods for solving the Volterra population growth model, a nonlinear integro-differential equation. The methods reduce the problem to algebraic equations and are shown to be applicable, but no concrete numerical improvements over existing methods are reported.
This paper aims to compare rational Chebyshev (RC) and Hermite functions (HF) collocation approach to solve the Volterra's model for population growth of a species within a closed system. This model is a nonlinear integro-differential equation where the integral term represents the effect of toxin. This approach is based on orthogonal functions which will be defined. The collocation method reduces the solution of this problem to the solution of a system of algebraic equations. We also compare these methods with some other numerical results and show that the present approach is applicable for solving nonlinear integro-differential equations.