Application and Numerical Simulation of Modelled Epidemical Problems as Ordinary Differential Equation Using New Computation Method
Year: 2026
Type: article
Abstract: This study presents the development and application of a New Computational Method (NCM) for the numerical simulation of epidemiological problems modelled as ordinary differential equations. The method was derived using power series polynomial approximations combined with interpolation and collocation techniques at selected grid and off-grid points. The resulting scheme was formulated as a one-step block method capable of solving first-order epidemiological differential equations efficiently. Fundamental numerical properties of the proposed method were investigated, including order, consistency, zero-stability, convergence, and absolute stability. The analysis revealed that the method possesses an order of eleven, thereby ensuring high accuracy. Furthermore, the method was shown to be consistent, zero-stable, and convergent according to Dahlquist’s convergence theorem. The region of absolute stability was obtained using the boundary locus technique, confirming the suitability of the method for the numerical integration of epidemiological models. To evaluate its performance, the NCM was applied to three representative epidemiological differential equation models, namely the Logistic Growth Model, the Decay Model and the Mixture Model. Numerical results obtained from the simulations were compared with exact analytical solutions and existing numerical methods reported in the literature. The computed solutions closely matched the exact solutions across all test problems and successfully reproduced the qualitative behaviour of the underlying models. The comparisons demonstrated that the NCM is highly reliable, efficient and robust for solving a wide range of epidemiological differential equations. Consequently, the NCM provides an effective computational tool for modelling and simulating disease-related and other applied mathematical phenomena governed by ordinary differential equations.
Institution: Adamawa State University
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
OpenAlex ID: W7203983428