Rastgele efektli fredholm ve volterra integral denklemerin çözüm davranışları
Erişim
info:eu-repo/semantics/openAccessTarih
2020Erişim
info:eu-repo/semantics/openAccessÜst veri
Tüm öğe kaydını gösterÖzet
Bu çalışmada, Fredholm, Volterra ve Volterra-İntegro integral denklemlerinin katsayıları ve başlangıç koşulları rastgele değişken seçilerek denklemler rastgele hale getirilmiştir. Bu denklemlerin çözümleri için yarı analitik yöntemlerden diferansiyel, Elzaki, Laplace ve Sumudu dönüşüm, varyasyonel iterasyon yöntemlerinin yanı sıra direkt ve seri çözüm yöntemleri de kullanılmıştır. Ayrıca, elde edilen rastgele Fredholm, Volterra ve Volterra-İntegro integral denklemlerin çözümleri bulunarak, çözümlerin olasılık karakteristikleri incelenmiştir. Parametreler farklı olasılık dağılımlarından seçilerek, örneğin Beta, Gamma, Üçgensel, Üstel, Düzgün, Normal dağılım olması durumunda çözümlerin beklenen değer ve varyansları hesaplanarak, grafiksel olarak gösterilmiştir. Anahtar Kelimeler: Beklenen Değer, Fredholm, Rastgele Değişken, Rastgele İntegral Denklem, Varyans, Volterra ve Volterra-İntegro İntegral Denklemler In this study, the coefficients and initial conditions of Fredholm, Volterra and Volterra-Integro integral equations were randomized by selecting random variables. For the solutions of these equations, the semi-analytical methods such as differential, Elzaki, Laplace and Sumudu transform, variational iteration methods as well as direct and serial solution methods were used. In addition, the solutions of the random Fredholm, Volterra and Volterra-Integro integral equations were found and the probability characteristics of the solutions were examined. Parameters are selected from different probability distributions, for example, in case of Beta, Gamma, Triangular, Exponential, Uniform, Normal distribution, the expected values and variances of the solutions are calculated and shown graphically. Keywords: Expected value, Fredholm, Random Variable, Random Integral Equation, Variance, Volterra and Volterra-İntegro integral equations
Bağlantı
https://tez.yok.gov.tr/UlusalTezMerkezi/TezGoster?key=8tbPippmWV_b-Irrn9YEAvYuHignTbbR-JC1w6NFgj5N6TlOoybrFH-VcekuSId6https://tez.yok.gov.tr/UlusalTezMerkezi/EkGoster?key=6ZtRe5rnHrr74rjfYBQv_vJhGlp4jUD1WklJ8qpr9yeXRF87Wd7231ojal68-vBj
https://hdl.handle.net/20.500.12440/2344
Koleksiyonlar
- Tez Koleksiyonu [611]
İlgili Öğeler
Başlık, yazar, küratör ve konuya göre gösterilen ilgili öğeler.
-
Solving Bigeometric Volterra Integral Equations by Using Successive Approximations Method
Güngör, Nihan (2021)In this study, the successive approximations method has been applied to investigate the solution for the linear bigeometric Volterra integral equations of the second kind in the sense of bigeometric calculus. The conditions ... -
Investigation of the Behaviour of Volterra Integral Equations with Random Effects
Merdan, Mehmet; Altay, Özge; Bekiryazıcı, Zafer (2020)In this study, random Volterra integral equations obtained by transforming components of deterministic Volterra integral equations to random variables are analysed. Beta, Normal (Gaussian), Gamma, Geometric and Uniform ... -
BG-Volterra Integral Equations and Relationship with BG-Differential Equations
Güngör, Nihan (2020)In this study, the Volterra integral equations are defined in the sense of bigeometric calculus by the aid of bigeometric integral. The main aim of the study is to research the relationship between bigeometric Volterra ...