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

Yıl: 2019 Cilt: 9 Sayı: 1 Sayfa Aralığı: 108 - 118 Metin Dili: İngilizce 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
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 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