Numerical approximations for population growth model by Rational Chebyshev and Hermite Functions collocation approach: A comparison

TL;DR

This paper compares rational Chebyshev and Hermite functions collocation methods for solving nonlinear population growth models modeled by Volterra's integro-differential equations, demonstrating their effectiveness and applicability.

Contribution

It introduces a comparative analysis of RC and HF collocation methods for nonlinear integro-differential equations in population models, highlighting their advantages.

Findings

Both methods effectively solve the nonlinear integro-differential equations.

The collocation approach reduces the problem to algebraic equations.

The methods outperform some existing numerical techniques.

Abstract

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.