| Abstract: |
| Nonlinear differential equations frequently arise in mathematical models describing viral infection dynamics, where analytical solutions are rarely available. Therefore, reliable numerical methods are required to approximate the behavior of such systems. In this study, we propose a numerical approach based on the Chebyshev collocation method for solving nonlinear systems appearing in HIV infection models.
The method approximates the solution components using Chebyshev polynomial expansions and enforces the governing equations at selected collocation points. This formulation transforms the original nonlinear differential system into a system of algebraic equations that can be solved efficiently using standard numerical techniques. Due to the spectral accuracy of Chebyshev polynomials, the proposed approach provides highly accurate approximations with relatively low computational cost.
To demonstrate the applicability of the method, we apply the proposed scheme to a three-dimensional HIV infection model describing the interaction between healthy cells, infected cells, and virus particles. Numerical simulations show that the method accurately captures the qualitative behavior of the system dynamics. In addition, the formulation suggests that the proposed collocation framework can be extended to models defined on time scales, providing a potential tool for studying systems involving both continuous and discrete temporal structures. |
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