OICC Press Mathematical Sciences 2251-7456 20 3 2026 09 30 High-Order Taylor Collocation Methods for Linear Matrix Differential Equations: Theory and Computation 10.57647/mathsci.2026.2003.16 EN Junjie Li Hunan College For Preschool Education, Changde 415000, China Journal Article 2026 09 30 The paper develops a numerical technique employing Taylor polynomial expansion and collocation to solve linear matrix differential equations of first order. The proposed technique converts the original differential matrix equation into a set of algebraic equations using matrix manipulations such as Kronecker products and vectorization of matrices. An error analysis is performed to show the sound theoretical background of the developed technique. Numerical investigations prove that the proposed Taylor collocation technique is more efficient than the Bernstein polynomial technique. Moreover, the accuracy and performance of the presented technique have been shown analytically as well as numerically.