KaydedilenlerDerginizi ekleyin

Dergiler / Konuralp Journal of Mathematics / 2026 / Volume: 4 Issue: 1

AN ALTERNATIVE TECHNIQUE FOR SOLVING ORDINARY DIFFERENTIAL EQUATIONS

Neşe Dernek
Fatih Aylıkçı
Sevil Kıvrak
Sayfa
—
Yayın Tarihi
2016-04-01
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Using obtained theorems, a few initial-value problems for ordinary di erential equations are solved as illustrations.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, a new method for solving ordinary di erential equations is given by using the generalized Laplace transform Ln.
📊
Temel Bulgular & Veri:Firstly, the authors introduce a di erential operator  that is called the -derivative.
💡
Sonuç & Katkı:Using obtained theorems, a few initial-value problems for ordinary di erential equations are solved as illustrations.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:The Laplace transform · The Ln-transform · The L􀀀1 n -transform and Linear ordinary di erential equations

Abstract

In this paper, a new method for solving ordinary di erential equations is given by using the generalized Laplace transform Ln. Firstly, the authors introduce a di erential operator  that is called the -derivative. A relation between the Ln-transform of the -derivative of a function and the Ln- transform of the function itself are derived. Then, the convolution theorem is proven. Using obtained theorems, a few initial-value problems for ordinary di erential equations are solved as illustrations.

🔖

Bu Makaleye Atıf Yap

Dernek, N., Aylıkçı, F., Kıvrak, S. (2016). AN ALTERNATIVE TECHNIQUE FOR SOLVING ORDINARY DIFFERENTIAL EQUATIONS. Konuralp Journal of Mathematics, Volume: 4 Issue: 1. https://ajindex.com/articles/1521898

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (13)

  1. A.,Aghili, A.,Ansari, A.,Sedghi, An inversion technique for the L2-transform with applica- tions, Int. J. Contemp. Math. Sciences, (2007), 2.28, 1387-1394.
  2. A.,Aghili, A.,Ansari, A new approach to solving SIEs and system of PFDEs using the L2- transform, Di erential Equations and Control Processes, (2010), N3, 1817-2172.
  3. L.,Debnath, The double Laplace Transforms and their properties with applications to func- tional, integral and partial di erential equations, International Journal of Applied and Computational Mathematics, (2015), 1-19.
  4. N.,Dernek, F.,Aylkc, Identities for the Ln-transform, The L2n-transform and the P2n- transform and their applications, Journal of Inequality and Special Functions, (2014), 5.4, 1-16.
  5. N.,Dernek, F.,Aylkc, Laplace ve L2 dnsmleriyle ksmi trevli denklemlerin czmleri, Marmara University, (2014), Master Thesis.
  6. D.G.,Du y, Transform methods for solving partial di erential equations, Symbolic and Numeric Computation, (2004).
  7. A.,Erdelyi, W.,Magnus, F.,Oberhettinger, F.G.,Tricomi, Tables of integral transforms Vol. 1, (1954), New York,NY,USA, McGraw-Hill.
  8. A.,Erdelyi, W.,Magnus, F.,Oberhettinger, F.G.,Tricomi, Tables of integral transforms Vol. 2, (1954), New York,NY,USA, McGraw-Hill.
  9. O.,Yurekli, Theorems on L2-transform and its applications, (1983), Vol.13 of Physical Sciences Data, Elsevier Scienti c Publishing Co., Amsterdam.
  10. O.,Yurekli, I.,Sadek, A Parseval-Goldstein type theorem on the Widder potential trans- form and its applications, International Journal of Mathematics and Mathematical Sciences, (1991), 14.3, 517-524.
  11. O.,Yurekli, S.,Wilson, A new method of solving Bessel's di erential equation using the L2- transform, Applied Mathematics and Computation, (2002), 130.2, 587-591.
  12. O.,Yurekli, S.,Wilson, A new method of solving Hermite's di erential equation using the L2-transform, Applied Mathematics and Computation, (2003), 145.2, 495-500.
  13. E.,Zauderer, Partial di erential equations of applied mathematics, (2004), John Wiley and Sons, Inc.