Journals Information
Mathematics and Statistics Vol. 13(5), pp. 345 - 353
DOI: 10.13189/ms.2025.130510
Reprint (PDF) (511Kb)
A Lagrange-Based Hybrid Block Method with Single Off-Step Point for Differential Equations within a Fuzzy Framework
Siti Syazwani Sazali 1, Nurul Huda Abdul Aziz 1,*, Muhammad Zaini Ahmad 1, Lee Khai Chien 2
1 Department of Mathematical Sciences, Faculty of Intelligent Computing, Universiti Malaysia Perlis (UniMAP), Kampus Alam UniMAP Pauh Putra, 02600 Arau, Perlis, Malaysia
2 Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia
ABSTRACT
This paper presents a novel and efficient two-step hybrid block scheme incorporating a single off-step point for solving differential equation with fuzzy numbers. Addressing the demand for robust and precise solvers designed specifically for fuzzy systems, the proposed approach leverages the adaptability of a two-step scheme enhanced by an additional evaluation at an off-step point to improve both accuracy and computational performance. The formulation of the 2HBM1OP algorithm is achieved through constructing a Lagrange interpolation polynomial that includes both step and off-step nodes, enabling the approximation of the fuzzy solution at multiple points within each computational block. A thorough convergence study confirms the method's consistency and zero-stability conditions are satisfied under fuzzy equations. Numerical tests involving benchmark fuzzy differential equations demonstrate the approach's effectiveness in achieving accurate results with efficient computational effort relative to exact solutions. This work contributes to the advancement of numerical techniques in fuzzy system analysis by providing a rigorously developed and practically applicable method that tackles the unique challenges inherent in fuzzy initial value problems. The 2HBM1OP scheme bridges theoretical fuzzy concepts with numerical computation and lays groundwork for future exploration of higher-order block methods in fuzzy settings.
KEYWORDS
Fuzzy Differential Equations, Off-Step Point, Hybrid Block Method, Convergence Analysis
Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Siti Syazwani Sazali , Nurul Huda Abdul Aziz , Muhammad Zaini Ahmad , Lee Khai Chien , "A Lagrange-Based Hybrid Block Method with Single Off-Step Point for Differential Equations within a Fuzzy Framework," Mathematics and Statistics, Vol. 13, No. 5, pp. 345 - 353, 2025. DOI: 10.13189/ms.2025.130510.
(b). APA Format:
Siti Syazwani Sazali , Nurul Huda Abdul Aziz , Muhammad Zaini Ahmad , Lee Khai Chien (2025). A Lagrange-Based Hybrid Block Method with Single Off-Step Point for Differential Equations within a Fuzzy Framework. Mathematics and Statistics, 13(5), 345 - 353. DOI: 10.13189/ms.2025.130510.