A Comparison of Three Methods Based on the Bernstein Operational Matrix for Solving Differential and Integral Equations

Year 2025, Early View, 1 - 1

Guliza Taalaybekova Mediha Örkcü

https://doi.org/10.35378/gujs.1619802

Abstract

This article investigates combining traditional methods for solving differential equations with Aboodh integral transformation and the Bernstein method. This approach offers a new perspective in solving various differential and integral equations. The solution approach obtained from the combination of Bernstein polynomials and integral transformations stands out in terms of theoretical and practical implications. This method can be applied to various examples of differential equations, and its practical applicability can be evaluated through studies conducted using programming languages. The error between the exact solution and the proposed method’s approximate solution has been calculated. We compare the numerical results of the Aboodh-Bernstein, Laplace-Bernstein, and Sumudu-Bernstein methods.

Keywords

Differential equation , Aboodh transform , Bernstein polynomials

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