Dirichlet Sınır Koşullu Diferansiyel Denklemlerin Bir Sınıfının Geometrik Ortalamalar Optimizasyonu Çözümleri

Year 2024, Volume: 1 Issue: 1, 19 - 29, 06.07.2024

İclal Gör , Türkan Özyörük

Abstract

Bu çalışma, matematiksel modellemede yaygın olarak karşılaşılan Dirichlet sınır koşullarını sağlayan diferansiyel denklemlerin çözümüne odaklanmaktadır. Bu denklemleri çözmek için Geometrik Ortalama Optimizasyonu (GMO) algoritması kullanılmıştır. Bu amaçla öncelikle ileri beslemeli yapay sinir ağı ile sınır koşullarının sağlanması için ön eğitimden geçirilmiş ve maliyet fonksiyonu minimize edilerek yapay sinir ağına ait ağırlık güncelleme işlemi gerçekleştirilmiştir. GMO algoritmasının kullanımı, geleneksel çözüm yöntemlerine bir alternatif olarak incelenmiş ve deneysel çalışmalarda benzer performans sağlamıştır. Bu amaçla, Dirichlet koşullarına sahip diferansiyel denklemlerin çözümü araştırılmıştır. Elde edilen sonuçlar, GMO algoritmasının Dirichlet koşullu diferansiyel denklemlerin çözümü için bir alternatif sunduğunu önermektedir.

Keywords

• Küresel optimizasyon, meta-sezgisel algoritma, geometrik ortalama optimizasyonu, dirichlet sınır koşulllu diferansiyel denklem

Thanks

Çalışmaya değerli katkılarından ötürü Doç. Dr. Korhan GÜNEL'e teşekkür ederiz.

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