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Dergiler / TWMS Journal of Applied and Engineering Mathematics / 2026 / Volume: 16 Issue: 1

A NUMERICAL SOLUTION TO NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS BASED ON BELL POLYNOMIALS

Kübra Erdem Biçer(MANİSA CELÂL BAYAR ÜNİVERSİTESİ)0000-0002-4998-6531
Gökçe Yıldız(MANİSA CELÂL BAYAR ÜNİVERSİTESİ)0000-0001-9896-6580
Sayfa
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Yayın Tarihi
2026-01-08
DOI
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Yapay Zeka Hızlı Bakış & Çıkarımlar

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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

For these examples, the Bell solutions and the absolute error functions are calculated, and the results are shown in tables and figures for comparison with the exact solutions.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:This article examines the solutions of high-order nonlinear ordinary differential equations with cubic terms under initial conditions using Bell polynomials, their derivatives, and collocation points.
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Temel Bulgular & Veri:To illustrate the method, some numerical examples are presented.
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Sonuç & Katkı:For these examples, the Bell solutions and the absolute error functions are calculated, and the results are shown in tables and figures for comparison with the exact solutions.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Nonlinear differential equation · Bell polynomial · Collocation Method

Abstract

This article examines the solutions of high-order nonlinear ordinary differential equations with cubic terms under initial conditions using Bell polynomials, their derivatives, and collocation points. The nonlinear differential equation and the corresponding conditions are transformed into matrix form by means of Bell polynomials and reduced to an algebraic system. From the solution of this system, the unknown Bell coefficients are determined. By substituting these coefficients, the approximate solution of the problem is expressed in terms of Bell polynomials. To illustrate the method, some numerical examples are presented. For these examples, the Bell solutions and the absolute error functions are calculated, and the results are shown in tables and figures for comparison with the exact solutions.

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Bu Makaleye Atıf Yap

Biçer, K. E., Yıldız, G. (2026). A NUMERICAL SOLUTION TO NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS BASED ON BELL POLYNOMIALS. TWMS Journal of Applied and Engineering Mathematics, Volume: 16 Issue: 1. https://ajindex.com/articles/1604274

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