10.57647/mathsci.2026.2003.16

High-Order Taylor Collocation Methods for Linear Matrix Differential Equations: Theory and Computation

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  • Junjie Li*1,
  1. Hunan College For Preschool Education, Changde 415000, China

Received: 2025-12-23

Revised: 2026-04-22

Accepted: 2026-05-07

Published in Issue 2026-09-30

Published Online: 2026-05-30

Copyright (c) 2026 Junjie Li (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Li, J. (2026). High-Order Taylor Collocation Methods for Linear Matrix Differential Equations: Theory and Computation. Mathematical Sciences, 20(3). https://doi.org/10.57647/mathsci.2026.2003.16
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Abstract

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.

Keywords

  • Taylor polynomials,
  • Linear differential matrix equations,
  • Collocation method,
  • Kronecker product,
  • Error analysis
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