Third-Kind Chebyshev Spectral Collocation Method for Solving Models of Two Interacting Biological Species

Abstract

This paper develops numerical methods for solving a system of two nonlinear integro-differential equations that arise in biological modeling. A spectral collocation method utilizing third-kind Chebyshev polynomials forms the basis of the solution methodology, which efficiently converts the integro-differential system into a collection of nonlinear algebraic equations. To guarantee precise and effective calculation, these algebraic equations are subsequently numerically solved using Newton’s method. In comparison to current methods, the suggested approach offers notable gains in computational efficiency and precision. The spectral collocation method’s accuracy is confirmed by contrasting the outcomes with those derived from other numerical methods that are published in the literature. To further illustrate the applicability, dependability, and computational efficiency of the suggested approach in resolving complicated biological systems, a number of illustrative instances are provided. The ability of spectral collocation techniques based on third-kind Chebyshev polynomials to solve integro-differential equations in a variety of scientific and engineering applications is highlighted by this work.