فهرست نشریات علمی دسترسی آزاد ایران

This paper analyzes systems of linear first-order ordinary differential equations (ODEs) with parametric coefficients‎, ‎a class of problems that arises in control theory‎, ‎optimization‎, ‎and applied mathematics‎. ‎We introduce the notion of a comprehensive solution system for such parametric ODEs, constructed using Gröbner systems from computer algebra‎. ‎ Our approach partitions the parameter space into finitely many cells and associates an explicit solution with each cell‎. ‎ Furthermore, ‎we present an algorithm that computes a comprehensive solution system for any given parametric system‎. ‎To address the computational challenges inherent in Gröbner systems‎, ‎we adopt the GES algorithm‎, ‎a parametric variant of Gaussian elimination‎, ‎which eliminates the need for Gröbner bases. This method builds upon the LDS algorithm proposed in 2017‎. ‎ Both algorithms have been implemented in Maple‎, ‎and we illustrate the structural framework of the main algorithm with a straightforward example. The results highlight the practicality and effectiveness of the proposed methods for solving parametric linear first-order ODE systems.