Title: Self-adjusting formulae for the solution of fuzzy differential equations with triangular fuzzy numbers

Authors: Joshua Sunday; Joel Nimyel Ndam; Anthony Chukwuemeka Onyekonwu

Addresses: Department of Mathematics, Faculty of Natural Sciences, University of Jos, Nigeria ' Department of Mathematics, Faculty of Natural Sciences, University of Jos, Nigeria ' Department of Mathematics Programme, National Mathematical Centre, Abuja, Nigeria

Abstract: It is a known fact that in modelling real world phenomena, differential equations are indispensable. Uncertainty, unfortunately intervene with such real world problems. The uncertainty may arise from measurement error, determining initial/boundary conditions or even deficient data. Modelling these problems in the form of fuzzy differential equations (FDEs) helps address such setbacks. This research focuses on deriving self-adjusting formulae (SAF) through the variable stepsize strategy for the solution of FDEs with triangular fuzzy numbers. The SAF, which is in the form of implicit block backward differentiation formulae (BBDF) was derived in such a way that it automatically adjusts the stepsize to fit the FDE under consideration. The BBDFs have been known for their unbounded region of absolute stability, thus making them suitable for solving FDEs. The results obtained showed that the SAF is computationally efficient, robust and reliable.

Keywords: backward differentiation formulae; convergence; fuzzy differential equation; FDE; H-difference; Hukuhara derivative; interval differential equations; mathematical models; triangular fuzzy number; variable stepsize; uncertainty.

DOI: 10.1504/IJMOR.2025.148879

International Journal of Mathematics in Operational Research, 2025 Vol.32 No.2, pp.145 - 178

Received: 12 Sep 2023
Accepted: 25 Dec 2023
Published online: 30 Sep 2025 *

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