Approximate Solutions of Hyperbolic Telegraph Equations Arising in Circuit Theory

Öz

In this study, the hyperbolic telegraph differential equation describing the behavior of certain wave-like phenomena, such as the transmission of signals along a telegraph line, is considered. Numerical solutions of a telegraph equation are computed by using various operator-difference schemes and physic-informed neural networks. The error analysis is performed, and the results are compared.

Anahtar Kelimeler

• Hyperbolic Equations
• Numerical Solution
• Error Analysis
• Difference Scheme
• Neural Network

Devre Teorisinde Ortaya Çıkan Hiperbolik Telgraf Denklemlerinin Yaklaşık Çözümleri

Öz

Bu çalışmada, telgraf hattı boyunca sinyallerin iletimi gibi belirli dalga benzeri olayların davranışını tanımlayan hiperbolik telgraf diferansiyel denklemi ele alınmıştır. Bir telgraf denkleminin sayısal çözümleri çeşitli operatör farkı şemaları ve fizik bilgili sinir ağları kullanılarak hesaplanmıştır. Hata analizi yapılmış ve sonuçlar karşılaştırılmıştır.

Anahtar Kelimeler

• Hiperbolik Denklemler
• Sayısal Çözüm
• Hata Analizi
• Fark Şeması
• Sinir Ağı

Kaynakça

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