Investigation of the Behaviour of Volterra Integral Equations with Random Effects
Yıl: 2020 Cilt: 10 Sayı: 1 Sayfa Aralığı: 205 - 216 Metin Dili: İngilizce DOI: 10.17714/gumusfenbil.586796 İndeks Tarihi: 15-02-2021
Investigation of the Behaviour of Volterra Integral Equations with Random Effects
Öz: In this study, random Volterra integral equations obtained by transforming components of deterministic Volterraintegral equations to random variables are analysed. Beta, Normal (Gaussian), Gamma, Geometric and Uniformdistributions are used to investigate the random behaviour of the solutions for Volterra integral equations under randomeffects. The random version of Differential Transformation Method (RDTM) is used to obtain an approximation to thesolution of the random Volterra integral equation. Using the approximate solutions, approximate expected values andapproximate variances are calculated. Some integro-differential equations, obtained by using random components withthe above mentioned distributions, are solved as numerical examples. Results are obtained in MAPLE and shown ingraphs. It is seen that random Differential Transformation Method is effective for the examination of random Volterraintegral equations. Comparison of the solutions is given to underline the accuracy of the method.
Anahtar Kelime: Volterra İntegral Denklemlerinin Rastgele Etkilerle Davranışlarının İncelenmesi
Öz: Bu çalışmada deterministik Volterra integral denklemlerinin bileşenlerinin rastgele değişkenlere dönüştürülmesi ile elde edilen rastgele Volterra integral denklemleri incelenmektedir. Volterra integral denklemlerinin rastgele etkiler altındaki rastgele davranışlarını incelemek için Beta, Normal, Gamma, Geometrik ve Düzgün dağılımlar kullanılmaktadır. Rastgele Volterra integral denkleminin çözümüne bir yaklaşım elde etmek için Diferansiyel Dönüşüm Yöntemi’nin rastgele versiyonu (RDTM) kullanılmaktadır. Yaklaşık çözüm kullanılarak yaklaşık beklenen değerler ve yaklaşık varyanslar hesaplanmaktadır. Bahsedilen dağılımlara sahip rastgele bileşenler kullanılarak elde edilen bazı integro-diferansiyel denklemler sayısal örnek olarak kullanılmaktadır. Sonuçlar MAPLE’da elde edilmiş ve grafiklerle gösterilmiştir. Rastgele Diferansiyel Dönüşüm Yöntemi’nin rastgele Volterra İntegral Denklemleri’nin incelenmesinde etkili bir araç olduğu görülmektedir. Yöntemin doğruluğunu göstermek için sonuçların karşılaştırmalarına yer verilmiştir.
Anahtar Kelime: Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
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| APA | Merdan M, ALTAY ö, Bekiryazıcı Z (2020). Investigation of the Behaviour of Volterra Integral Equations with Random Effects. , 205 - 216. 10.17714/gumusfenbil.586796 |
| Chicago | Merdan Mehmet,ALTAY özge,Bekiryazıcı Zafer Investigation of the Behaviour of Volterra Integral Equations with Random Effects. (2020): 205 - 216. 10.17714/gumusfenbil.586796 |
| MLA | Merdan Mehmet,ALTAY özge,Bekiryazıcı Zafer Investigation of the Behaviour of Volterra Integral Equations with Random Effects. , 2020, ss.205 - 216. 10.17714/gumusfenbil.586796 |
| AMA | Merdan M,ALTAY ö,Bekiryazıcı Z Investigation of the Behaviour of Volterra Integral Equations with Random Effects. . 2020; 205 - 216. 10.17714/gumusfenbil.586796 |
| Vancouver | Merdan M,ALTAY ö,Bekiryazıcı Z Investigation of the Behaviour of Volterra Integral Equations with Random Effects. . 2020; 205 - 216. 10.17714/gumusfenbil.586796 |
| IEEE | Merdan M,ALTAY ö,Bekiryazıcı Z "Investigation of the Behaviour of Volterra Integral Equations with Random Effects." , ss.205 - 216, 2020. 10.17714/gumusfenbil.586796 |
| ISNAD | Merdan, Mehmet vd. "Investigation of the Behaviour of Volterra Integral Equations with Random Effects". (2020), 205-216. https://doi.org/10.17714/gumusfenbil.586796 |
| APA | Merdan M, ALTAY ö, Bekiryazıcı Z (2020). Investigation of the Behaviour of Volterra Integral Equations with Random Effects. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, 10(1), 205 - 216. 10.17714/gumusfenbil.586796 |
| Chicago | Merdan Mehmet,ALTAY özge,Bekiryazıcı Zafer Investigation of the Behaviour of Volterra Integral Equations with Random Effects. Gümüşhane Üniversitesi Fen Bilimleri Dergisi 10, no.1 (2020): 205 - 216. 10.17714/gumusfenbil.586796 |
| MLA | Merdan Mehmet,ALTAY özge,Bekiryazıcı Zafer Investigation of the Behaviour of Volterra Integral Equations with Random Effects. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, vol.10, no.1, 2020, ss.205 - 216. 10.17714/gumusfenbil.586796 |
| AMA | Merdan M,ALTAY ö,Bekiryazıcı Z Investigation of the Behaviour of Volterra Integral Equations with Random Effects. Gümüşhane Üniversitesi Fen Bilimleri Dergisi. 2020; 10(1): 205 - 216. 10.17714/gumusfenbil.586796 |
| Vancouver | Merdan M,ALTAY ö,Bekiryazıcı Z Investigation of the Behaviour of Volterra Integral Equations with Random Effects. Gümüşhane Üniversitesi Fen Bilimleri Dergisi. 2020; 10(1): 205 - 216. 10.17714/gumusfenbil.586796 |
| IEEE | Merdan M,ALTAY ö,Bekiryazıcı Z "Investigation of the Behaviour of Volterra Integral Equations with Random Effects." Gümüşhane Üniversitesi Fen Bilimleri Dergisi, 10, ss.205 - 216, 2020. 10.17714/gumusfenbil.586796 |
| ISNAD | Merdan, Mehmet vd. "Investigation of the Behaviour of Volterra Integral Equations with Random Effects". Gümüşhane Üniversitesi Fen Bilimleri Dergisi 10/1 (2020), 205-216. https://doi.org/10.17714/gumusfenbil.586796 |
