A generalized classical method analysis of transient regimes in nonlinear electrical circuits by using differential taylor transform

Öz

In this study, we consider the Generalized Classical (GC) method based on the differential Taylor (DT) transform method for the analysis of transient regimes in simple electrical circuits. The approximate solution of nonlinear differential equations of electrical circuits with variable coefficients is found by using the GC method. It is shown that, if the solution is decomposed as steady-state and the temporary components, the use of the GC method can become more advantageous, and the transient differential equation of the circuits can be analyzed without a fully solving process. The efficiency of the considered method is illustrated by compared with the results obtained from similar problems in the literature. The results reveal that the proposed method is very effective and simple and can be applied to the analysis of both linear and nonlinear problems in physical systems. The short history and real status of the DT transform method are mentioned briefly.

Anahtar Kelimeler

• Differential Taylor transform
• Differential spectrums
• Generalized classical method
• Electrical circuit
• Transient regimes
• Differential equations

Diferansiyel taylor dönüşümü kullanılarak doğrusal olmayan elektrik devrelerinde geçici rejimlerin genelleştirilmiş klasik yöntem analizi

Öz

Bu çalışmada, basit elektrik devrelerinde geçici rejimlerin analizi için diferansiyel Taylor (DT) dönüşümü yöntemini temel alan Genelleştirilmiş Klasik (GK) yöntemini ele alıyoruz. Değişken katsayılı elektrik devrelerinin doğrusal olmayan diferansiyel denklemlerinin yaklaşık çözümü GK yöntemi kullanılarak bulunur. Çözümün kararlı durum ve geçici bileşenler olarak ayrıştırılması durumunda GK yönteminin kullanımının daha avantajlı hale gelebileceği ve devrelerin geçici diferansiyel denkleminin tam bir çözme işlemi olmadan analiz edilebileceği gösterilmiştir. Ele alınan yöntemin etkinliği literatürdeki benzer problemlerden elde edilen sonuçlarla karşılaştırılarak gösterilmiştir. Sonuçlar, önerilen yöntemin çok etkili ve basit olduğunu ve fiziksel sistemlerdeki hem doğrusal hem de doğrusal olmayan problemlerin analizine uygulanabileceğini ortaya koymaktadır. DT dönüşüm yönteminin kısa tarihçesi ve gerçek durumundan kısaca bahsedilmiştir.

Anahtar Kelimeler

• Diferansiyel Taylor dönüşümü
• Diferansiyel spektrumlar
• Genelleştirilmiş klasik yöntem
• Elektrik devresi
• Geçici rejimler
• Diferansiyel denklemler

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