University of Tabriz Computational Methods for Differential Equations 2345-3982 11 3 2023 06 01 Numerical methods for m-polar fuzzy initial value problems 412 439 15844 10.22034/cmde.2023.50105.2083 EN Muhammad Saqib Department of Mathematics, University of Gujrat, Gujrat, Pakistan. Muhammad Akram Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan. Shahida Bashir Department of Mathematics, University of Gujrat, Gujrat, Pakistan. Tofigh Allahviranloo Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey. Journal Article 2022 01 27 Some problems in science and technology are modeled using ambiguous, imprecise, or lacking contextual data. In the modeling of some real-world problems, differential equations often involve multi-agent, multi-index, multi-objective, multi-attribute, multi-polar information or uncertainty, rather than single bits. These types of differentials are not well represented by fuzzy differential equations or bipolar fuzzy differential equations. Therefore, m-pole fuzzy set theory can be applied to differential equations to deal with problems with multi-polar information. In this paper, we study differential equations in m extremely fuzzy environments. We introduce the concept gH-derivative of m-polar fuzzy valued function. By considering different types of differentiability, we propose some properties of the gH-differentiability of m-polar fuzzy-valued functions. We consider the m-polar fuzzy Taylor expansion. Using Taylor expansion, Euler's method and modified Euler's method for solving the m-polar fuzzy initial value problem are proposed. We discuss the convergence analysis of these methods. Some numerical examples are described to see the convergence and stability of the proposed method. We compare these methods by computing the global truncation error. From the numerical results, it can be seen that the modified Euler method converges to the exact solution faster than the Euler method. Generalized Hukuhara derivative Taylor expansion Initial value problem Convergence analysis https://cmde.tabrizu.ac.ir/article_15844_30b921f2c23427c70b145d7e1eccaebe.pdf