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Journals / Sakarya University Journal of Science / 2026 / Volume: 21 Issue: 3

Numerical Approach for the two-dimensional heat equation problem with convective boundary conditions

İki-Boyutlu Konvektif Sınır Koşullu Erime Problemi İçin Nümerik Yaklaşım

Vildan Gülkaç
Pages
—
Publication Date
2017-06-01
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The results of computing by present procedure are in totally compatible with the results obtained previously by other researches.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this work, we extended our earlier study on the solution of two-dimensional heat equation problem by considering a class of time-split finite difference methods.
📊
Key Findings & Data:The procedure is second order accurate in time and in (x, y) coordinates.
💡
Conclusion & Impact:The results of computing by present procedure are in totally compatible with the results obtained previously by other researches.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Flux limiters · LOD method · ADI method

Abstract

In this work, we extended our earlier study on the solution of two-dimensional heat equation problem by considering a class of time-split finite difference methods. Operator splitting is used as a procedure for computing, some derivatives are computed explicitly and some of them computed implicitly during this procedure. The procedure is second order accurate in time and in (x, y) coordinates. The results of computing by present procedure are in totally compatible with the results obtained previously by other researches.

Özet

Bu çalışmada, daha önce çözdüğümüz, iki-boyutlu konvektif sınır koşullu erime probleminde, türevlerin bir kısmında açık yöntem kullanırken bir kısmında da kapalı yöntem kullanarak sonlu farklar oluşturulmuştur ve bu denklemlerin çözümü için bir iteratif yöntem geliştirilmiştir. Metod (x, y) koordinatlarında ikinci dereceden doğruluğa sahiptir. Bu metodla elde edilen sonuçlar, önceki araştırmacılar tarafından verilen sonuçlarla tamamen uyumludur.

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Cite This Article

Gülkaç, V. (2017). Numerical Approach for the two-dimensional heat equation problem with convective boundary conditions. Sakarya University Journal of Science, Volume: 21 Issue: 3. https://doi.org/10.16984/saufenbilder.283775

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