Mathematics and Computational Sciences

A Hybrid Collocation–Least Squares Scheme for the Accurate Integration of Stiff ODEs

Articles in Press

Document Type : Original Article

Authors

Mohammad Taghi Darvishi 1
Samad Kheybari 2
Younes Salehi 1
Farzaneh Alizadeh 3
Kamyar Hosseini 4

1 Department of Mathematics, Razi University, Kermanshah 67149, Iran

2 Faculty of Art and Science, University of Kyrenia, TRNC, Mersin 10, Kyrenia 99320, Turkey

3 Department of Mathematics, Near East University, TRNC, Mersin 10, Nicosia 99138, Turkey

4 Mathematics Research Center, Near East University, TRNC, Mersin 10, Nicosia 99138, Turkey

https://doi.org/10.30511/mcs.2026.2073486.1489
Abstract
This study introduces a mathematical framework for solving initial value problems (IVPs) through a hybrid numerical strategy that integrates collocation techniques with a least-squares minimization scheme. The analytical foundation of the method is thoroughly developed, offering a systematic approach to address complex ordinary differential equations (ODEs).

The practical effectiveness of the proposed method is evaluated using a diverse set of benchmark problems, including stiff and high-order ODEs. The results demonstrate high accuracy and computational efficiency, with robust performance across different levels of problem complexity. Comparative analysis with established numerical techniques highlights the method’s reliability and positions it as a compelling alternative for tackling challenging IVPs.

Keywords

Ordinary differential equations
Initial value problems
Legendre polynomials
Chebyshev polynomials
Subjects
Mathematics and Computational Sciences

Articles in Press, Accepted Manuscript
Available Online from 29 September 2026

  • Receive Date 03 October 2025
  • Revise Date 08 September 2026
  • Accept Date 14 September 2026

Home

Submit Manuscript

Reviewers

Contact Us