Solving of Some Random Partial Differential Equations by Using Differential Transformation Method and Laplace- Padé Method

Mehmet MERDAN, (Gümüşhane University, Faculty of Engineering and Natural Sciences, Department of Mathematical Engineering, Gümüşhane, Türkiye)
Halil ANAÇ, (Gümüşhane University, Faculty of Engineering and Natural Sciences, Department of Mathematical Engineering, Gümüşhane, Türkiye)
Zafer BEKİRYAZICI, (Recep Tayyip Erdogan University, Faculty of Arts And Sciences, Department of Mathematics, Rize, Türkiye)
Tülay KESEMEN (Karadeniz Teknik Üniversitesi, Fen Fakültesi, Matematik Bölümü, Trabzon, Türkiye)
Gümüşhane Üniversitesi Fen Bilimleri Dergisi
11 0
Yıl: 2019 Cilt: 9 Sayı: 1 Sayfa Aralığı: 108 - 118 Metin Dili: İngilizce DOI: 10.17714/gumusfenbil.404332 İndeks Tarihi: 24-10-2019

Solving of Some Random Partial Differential Equations by Using Differential Transformation Method and Laplace- Padé Method

Öz:
In this study, the solutions of random partial differential equations are examined. The parameters and the initialconditions of the random component partial differential equations are investigated with Beta distribution. A fewexamples are given to illustrate the efficiency of the solutions obtained with the random Differential TransformationMethod (rDTM). Functions for the expected values and the variances of the approximate analytical solutions of therandom equations are obtained. Random Differential Transformation Method is applied to examine the solutions ofthese partial differential equations and MAPLE software is used for the finding the solutions and drawing the figures.Also the Laplace- Padé Method is used to improve the convergence of the solutions. The results for the randomcomponent partial differential equations with Beta distribution are analysed to investigate effects of this distribution onthe results. Random characteristics of the equations are compared with the results of the deterministic partial differentialequations. The efficiency of the method for the random component partial differential equations is investigated bycomparing the formulas for the expected values and variances with results from the simulations of the randomequations.
Anahtar Kelime:

Konular: Tarımsal Ekonomi ve Politika Ziraat Mühendisliği Bitki Bilimleri

Bazı Rastgele Kısmi Diferansiyel Denklemlerin Diferansiyel Dönüşüm Metodu ve Laplace- Padé Metodu Kullanarak Çözümü

Öz:
Bu çalışmada, rastgele kısmi diferansiyel denklemlerin çözümleri incelenmiştir. Rastgele bileşenli kısmi diferansiyel denklemlerin başlangıç şartları ve parametreleri Beta dağılımı ile incelenmiştir. Rastgele Diferansiyel dönüşüm yöntemi ile elde edilen çözümlerin etkinliği birkaç örnekle verilmiştir. Rastgele denklemlerin yaklaşık analitik çözümlerinin beklenen değerleri ve varyansları için fonksiyonlar elde edilmiştir. Rastgele Diferansiyel dönüşüm yöntemi, bu kısmi diferansiyel denklemlerin çözümlerini incelemek için uygulanmış ve MAPLE programı, çözümleri bulmak ve grafikleri çizmek için kullanılmıştır. Ayrıca çözümlerin yakınsaklığını iyileştirmek için Laplace-Padé metodu kullanılmıştır. Beta dağılımı ile rastgele bileşenli kısmi diferansiyel denklemlerin sonuçları, bu dağılımın sonuçlara etkilerini incelemek amacıyla analiz edilmiştir. Denklemlerin rastgele karakteristikleri ile rastgele olmayan kısmi diferansiyel denklemlerin sonuçları karşılaştırılmıştır. Rastgele bileşenli kısmi diferansiyel denklemler için yöntemin etkinliği, rastgele denklemlerin simülasyonlarından elde edilen sonuçlarla beklenen değerlerin ve varyansların formüllerini karşılaştırarak incelenmiştir. MAPLE programı, rastgele bileşenli kısmi diferansiyel denklemlerin sonuçlarını simüle etmek için kullanılmıştır ve bu simülasyon sonuçlarından standart sapma, güven aralığı gibi diğer karakteristiklerler elde edilmiştir
Anahtar Kelime:

Konular: Tarımsal Ekonomi ve Politika Ziraat Mühendisliği Bitki Bilimleri
Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • Abassy, T.A., El-Tawil, M.A. and El-Zoheiry, H., 2007. Exact Solutions of Some Nonlinear Partial Differential Equations Using the Variational Iteration Method Linked with Laplace Transforms and the Pade Technique. Computers and Mathematics with Applications, 54, 940-954.
  • Bildik, N., Konuralp, A., Bek, F.O. and Küçükarslan, S., 2006. Solution of Different Type of the Partial Differential Equation by Differential Transform Method and Adomian’s Decomposition Method. Applied Mathematics and Computation, 172(1), 551-567.
  • Eugene, N., Lee, C. and Femoye, F., 2002. Beta-Normal Distribution and Its Applications. Communications in Statistics-Theory and Methods, 31(4), 497-512.
  • Hadizadeh, M. and Moatamedi, N., 2007. A New Differential Transformation Approach for Two-Dimensional Volterra Integral Equations, International Journal of Computer Mathematics, 84(4), 515-526.
  • Jang, M.J., Chen, C.L. and Liu, Y.C., 2001. Two-Dimensional Differential Transform for Partial Differential Equations. Applied Mathematics and Computation, 121(2-3), 261-270.
  • Kangalgil, F. and Ayaz, F., 2009. Solitary Wave Solutions for the KdV and mKdV Equations by Differential Transform Method. Chaos, Solitons and Fractals, 41, 464-472.
  • Kanth, R.A.S.V. and Aruna, K., 2009. Two- Dimensional Differential Transform Method for Solving Linear and Non-linear Schrödinger Equations. Chaos, Solitons and Fractals, 41, 2277-2281.
  • Khalaf, S.L., 2011. Mean Square Solutions of Second-Order Random Differential Equations by Using Homotopy Perturbation Method. International Mathematical Forum, 6, 2361-2370.
  • Khudair, A.R., Ameen, A.A. and Khalaf, S.L., 2011. Mean Square Solutions of Second-Order Random Differential Equations by Using Adomian Decomposition Method. Applied Mathematical Sciences, 5, 2521-2535.
  • Khudair, A.R., Ameen, A.A. and Khalaf, S.L., 2011. Mean Square Solutions of Second-Order Random Differential Equations by Using Variational Iteration Method. Applied Mathematical Sciences, 5, 2505-2519.
  • Khudair, A.R., Haddad, S.A.M. and Khalaf, S.L., 2016. Mean Square Solutions of Second-Order Random Differential Equations by Using the Differential Transformation Method. Open Journal of Applied Sciences, 6, 287-297.
  • Merdan, M., 2010. A New Application of Modified Differential Transformation Method for Modelling the Pollution of a System of Lakes. Selçuk Journal of Applied Mathematics, 11(2), 27-40.
  • Pukhov, G.E., 1982. Differential Transforms and Circuit Theory. Circuit Theory and Applications. 10, 265-276.
  • Tari, A., Rahimi, M.Y., Shahmorad, S. and Talati, F., 2009. Solving a Class of Two-Dimensional Linear and Nonlinear Volterra Integral Equaitons by the Differential Transform Method. Journal of Computational and Applied Mathematics, 228, 70-76.
  • Villafuerte, L. and Chen-Charpentier, B.M., 2012. A Random Differential Transform Method: Theory and Applications, Applied Mathematics Letters, 25(10), 1490-1494.
  • Yüzbaşi, Ş. and Ismailov, N., 2017. Differential Transform Method to Solve Two-Dimensional Volterra Integral Equations with Proportional Delays. New Trends in Mathematical Sciences, 5(4), 65-71.
  • Zhou, J.K., 1986. Differential Transformation and Its Applications for Electrical Circuits, Huazhong University Press, Wuhan.
  • Ziyaee, F. and Tari, A., 2015. Differential Transform Method for Solving the Two-Dimensional Fredholm Integral Equations. Applications and Applied Mathematics, 10(2), 852-863.
APA MERDAN M, ANAÇ H, Bekiryazıcı Z, KESEMEN T (2019). Solving of Some Random Partial Differential Equations by Using Differential Transformation Method and Laplace- Padé Method. , 108 - 118. 10.17714/gumusfenbil.404332
Chicago MERDAN Mehmet,ANAÇ Halil,Bekiryazıcı Zafer,KESEMEN Tülay Solving of Some Random Partial Differential Equations by Using Differential Transformation Method and Laplace- Padé Method. (2019): 108 - 118. 10.17714/gumusfenbil.404332
MLA MERDAN Mehmet,ANAÇ Halil,Bekiryazıcı Zafer,KESEMEN Tülay Solving of Some Random Partial Differential Equations by Using Differential Transformation Method and Laplace- Padé Method. , 2019, ss.108 - 118. 10.17714/gumusfenbil.404332
AMA MERDAN M,ANAÇ H,Bekiryazıcı Z,KESEMEN T Solving of Some Random Partial Differential Equations by Using Differential Transformation Method and Laplace- Padé Method. . 2019; 108 - 118. 10.17714/gumusfenbil.404332
Vancouver MERDAN M,ANAÇ H,Bekiryazıcı Z,KESEMEN T Solving of Some Random Partial Differential Equations by Using Differential Transformation Method and Laplace- Padé Method. . 2019; 108 - 118. 10.17714/gumusfenbil.404332
IEEE MERDAN M,ANAÇ H,Bekiryazıcı Z,KESEMEN T "Solving of Some Random Partial Differential Equations by Using Differential Transformation Method and Laplace- Padé Method." , ss.108 - 118, 2019. 10.17714/gumusfenbil.404332
ISNAD MERDAN, Mehmet vd. "Solving of Some Random Partial Differential Equations by Using Differential Transformation Method and Laplace- Padé Method". (2019), 108-118. https://doi.org/10.17714/gumusfenbil.404332
APA MERDAN M, ANAÇ H, Bekiryazıcı Z, KESEMEN T (2019). Solving of Some Random Partial Differential Equations by Using Differential Transformation Method and Laplace- Padé Method. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, 9(1), 108 - 118. 10.17714/gumusfenbil.404332
Chicago MERDAN Mehmet,ANAÇ Halil,Bekiryazıcı Zafer,KESEMEN Tülay Solving of Some Random Partial Differential Equations by Using Differential Transformation Method and Laplace- Padé Method. Gümüşhane Üniversitesi Fen Bilimleri Dergisi 9, no.1 (2019): 108 - 118. 10.17714/gumusfenbil.404332
MLA MERDAN Mehmet,ANAÇ Halil,Bekiryazıcı Zafer,KESEMEN Tülay Solving of Some Random Partial Differential Equations by Using Differential Transformation Method and Laplace- Padé Method. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, vol.9, no.1, 2019, ss.108 - 118. 10.17714/gumusfenbil.404332
AMA MERDAN M,ANAÇ H,Bekiryazıcı Z,KESEMEN T Solving of Some Random Partial Differential Equations by Using Differential Transformation Method and Laplace- Padé Method. Gümüşhane Üniversitesi Fen Bilimleri Dergisi. 2019; 9(1): 108 - 118. 10.17714/gumusfenbil.404332
Vancouver MERDAN M,ANAÇ H,Bekiryazıcı Z,KESEMEN T Solving of Some Random Partial Differential Equations by Using Differential Transformation Method and Laplace- Padé Method. Gümüşhane Üniversitesi Fen Bilimleri Dergisi. 2019; 9(1): 108 - 118. 10.17714/gumusfenbil.404332
IEEE MERDAN M,ANAÇ H,Bekiryazıcı Z,KESEMEN T "Solving of Some Random Partial Differential Equations by Using Differential Transformation Method and Laplace- Padé Method." Gümüşhane Üniversitesi Fen Bilimleri Dergisi, 9, ss.108 - 118, 2019. 10.17714/gumusfenbil.404332
ISNAD MERDAN, Mehmet vd. "Solving of Some Random Partial Differential Equations by Using Differential Transformation Method and Laplace- Padé Method". Gümüşhane Üniversitesi Fen Bilimleri Dergisi 9/1 (2019), 108-118. https://doi.org/10.17714/gumusfenbil.404332
Sayfa Oluşturulma Tarihi
23-04-2024 9:8

İLETİŞİM

TÜBİTAK ULAKBİM TR Dizin

Yüzüncüyıl, İşçi Blokları Mahallesi

Muhsin Yazıcıoğlu Caddesi No:51/C

06530 Çankaya / ANKARA +90 (312) 298 92 00

trdizin@tubitak.gov.tr

TÜBİTAK ULAKBİM Ulusal Akademik Ağ ve Bilgi Merkezi Cahit Arf Bilgi Merkezi © Tüm Hakları Saklıdır. Gizlilik Politikası Kullanım Şartları