Kesir mertebeden rastgele adi diferansiyel denklemlerin Adomian Ayrıştırma Yöntemi ile analizi

Abstract

Bu çalışmada, adi diferansiyel denklemlerin katsayılarının veya başlangıç koşullarının rasgele seçilmesiyle elde edilen rasgele adi diferansiyel denklemler, Adomian Ayrıştırma Yöntemi ile analiz edilecektir. Denklemlerin başlangıç koşulları veya katsayıları, normal ve üstel dağılıma sahip rasgele değişkenlere dönüştürülecektir. Elde edilen rastgele adi diferansiyel denklemlerin beklenen değeri, varyansı ve güven aralığı gibi olasılık özellikleri hesaplanacaktır. Elde edilen sonuçlar MATLAB (2013a) paket programı yardımıyla çizilecek ve rastgele sonuçlar yorumlanacaktır.

Keywords

• Adomian ayrıştırma yöntemi
• kesirli türev
• lineer olmayan adi diferansiyel denklem

Analysis of fractional random ordinary differential equations by Adomian Decomposition Method

Abstract

In this study, random ordinary differential equations obtained by randomly choosing the coefficients or initial conditions of the ordinary differential equations will be analyzed by the Adomian Decomposition Method. The initial conditions or coefficients of the equations will be converted to random variables with normal and exponential distribution. Probability characteristics such as expected value, variance and confidence interval of the obtained random ordinary differential equations will be calculated. Obtained results will be drawn with the help of MATLAB (2013a) package program and random results will be interpreted.

Keywords

• Adomian decomposition method
• fractional derivative
• nonlinear ordinary differantial equation

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