Doğrusal Olmayan Tekil Sınır Değer Problemlerinin Chebyshev Sonlu Farklar Yöntemi ile Çözümü

Abstract

Chebyshev Sonlu Farklar Yöntemi (CSFY) ile doğrusal olmayan tekil sınır değer problemleri çözülmüştür. Ayrıca yöntemin hata ve yakınsama analizi verilmiştir. Yöntemin yakınsaklığını ve etkinliğini göstermek için termal patlamada, küresel bir hücrede kararlı hal oksijen difüzyonunda ve izotermal gaz kürelerinin dengesinde ortaya çıkan gerçek mühendislik problemleri incelenmiştir. Sonuçlar, sunulan yöntemin problemi alt aralıklara bölmeksizin ve farklı sınır koşulları için farklı değişiklikler yapmaksızın doğruluğu yüksek ve çözüme oldukça hızlı yakınsadığını göstermektedir.

Keywords

• Chebyshev Polinomları
• Chebyshev Sonlu Farklar Yöntemi
• Doğrusal olmayan Tekil Sınır Değer Problemi
• Lane-Emden denklemi.

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