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Abstract

The F-transform is an effective tool in numerical mathematics that simplifies problem solving by transforming problems from the space of continuous functions into a finite-dimensional vector space. The aim of this study is to investigate the application of the F-transform in the numerical solution of second-order ordinary differential equations. In this work, the F-transform method is applied to solve initial value problems, two-point boundary value problems, and singular second-order differential equations. The research methodology is based on the development of numerical algorithms for approximating the solutions of linear and nonlinear second-order problems, along with the use of the inverse transform to obtain approximate solutions. The results demonstrate that, compared to classical methods such as the finite difference method, the proposed approach exhibits satisfactory accuracy and stability. Moreover, the convergence of F-transform-based methods is proven, and their efficiency is confirmed.

Keywords

Approximate Solution Convergence Analysis Fuzzy Transform Numerical Methods Second Order Differential Equation

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Zahir, A. F. (2026). Numerical Solution of Second-Order Initial and Boundary Value Problems Using Fuzzy Transform. Journal of Natural Sciences – Kabul University, 9(1), 105–136. https://doi.org/10.62810/jns.v9i1.466
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