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Stream/Area:
-
Subject:
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Paper ID:
IJSREM67041
Volume:
10 |
8 |
Aug 2026
Pages:
1-13
Publication Frequency:
Monthly (12 issues per year)
License:International Journal of Scientific Research in Engineering and Management follows the Creative Commons Attribution 4.0 (CC BY 4.0) License, allowing free use and distribution with proper attribution.
Mathematics
Smt. Kasturbai Walchand College of Art’s and Science, Sangli, Maharashtra, India
Mathematics
Smt. Kasturbai Walchand College of Art’s and Science, Sangli, Maharashtra, India
The use of differential equations has become an essential technique in modelling real-world situations with n number of solutions. Previously, to solve differential equations, numerical approaches based on the finite difference method and the approximation method were utilized. These approaches raised an issue of complexity in solving equations, as well as the issue of an unlimited number of iterations, which increased the time required to discover accurate solutions for systems. This study focused on the challenge of estimating the solvability of a linear and non-linear system for nth order equations using the Fuzzy transform. The fuzzy transform is built as an ordinary algebra type, with its member functions modified using an enhanced Euler's technique and followed by a trapezoidal rule. The basic idea behind this proposed approach is that it splits the equations into equal intervals and uses direct fuzzy transform to estimate the value before using inverse fuzzy to get the exact solution. Theorems are used to determine the best approximation of the given approach and are therefore proven. Thus, in this research, the Modified Fuzzy Transform (MFT) has been presented and implemented in MATLAB to provide precise solutions to specified differential equations. Its efficiency was evaluated, and it was discovered that it was more effective with negligible error than prior approaches.
KEYWORDS
The aim of this work is to provide an alternate way for solving Differential Equations of order. This study will focus on a numerical algorithm that will employ the Fuzzy transform as a technique to estimate the solution of Ordinary Differential Equations for both linear and nonlinear case. The numerical approach will be thoroughly explored and used to several instances with uniform and non-uniform partitions. Then direct and inverse MFT has been applied to obtain the exact solution. The results demonstrate that the MFT is an effective technique for estimating the solution of Differential Equations.
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Publication Date
8/31/2026
Peer Review Type
Double-Blind Peer Review
Review Rounds: 2
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