Parameterized Differential Transform Method and Its Application to Boundary Value Transmission Problems

Year 2023, Volume: 28 Issue: 2, 412 - 423, 31.08.2023

Merve Yücel , Fahreddin Muhtarov

https://doi.org/10.53433/yyufbed.1143699

Abstract

In this study, we developed a new modification of the well-known differential transform method (DTM) that differs from the classical one by the algorithm for calculating the coefficients of an approximate solution given as a series. The proposed new algorithm we will call α-parameterized DTM (α-p DTM,for short). By using the proposed α-p DTM, we solve the boundary value transmission problem for the third-order differential equation. For the same problem, an approximate solution is also found using also the classical DTM. The solutions obtained were compared graphically.

Keywords

Boundary value problems, Differential transform method, Transmission conditions

Thanks

"This paper was presented in 4th International Conference on Pure and Applied Mathematics (ICPAM - VAN 2022), Van-Turkey, June 22-23, 2022."

Parametreli Diferansiyel Dönüşüm Yöntemi ve Sınır Değer Geçiş Problemlerine Uygulanması

Abstract

Bu çalışmada literatürden iyi bilinen diferansiyel dönüşüm yönteminin (DDY) yeni bir modifikasyonunu geliştirdik. Seri biçiminde verilmiş yaklaşık çözümde serinin katsayılarının hesaplanmasında uyguladığımız algoritma geleneksel DDY’den farklıdır. Önerdiğimiz yeni algoritmayı α-parametreli diferansiyel dönüşüm yöntemi (α-p DDY) olarak adlandırıyoruz. Geliştirdiğimiz α-p DD yöntemini uygulayarak 3. mertebeden diferensiyel denklem için sınır değer geçiş probleminin yaklaşık çözümleri bulunmuştur. Aynı problemin başka bir yaklaşık çözümü, geleneksel DD yöntemi ile de bulunmuştur. Bulduğumuz sonuçlar grafiksel olarak karşılaştırılmıştır.

Keywords

Diferensiyel dönüşüm yöntemi, Geçiş şartları, Sınır-değer preblemleri

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