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- W122103775 abstract "We consider numerical methods for finding approximate solutions to Ordinary Differential Equations (ODEs) with parameters distributed with some probability by the Generalized Polynomial Chaos (GPC) approach. In particular, we consider those with forcing functions that have a random parameter in both the scalar and vector case. We then consider linear systems of ODEs with deterministic forcing and randomness in the matrix of the systems and conclude with a method of approximating solutions to the case where the system involves a nonlinear function of a matrix and a random variable. Acknowledgements I would like to give special thanks to my advisor Dr. Nathan Gibson for his guidance and support throughout the process of writing and editing this paper. Without Dr. Gibson’s expertise and assistance I would have suffered greatly. I also wish to express my gratitude to my committee members Dr. Vrushali Bokil and Dr. Malgorzata Peszynska for kindly giving my their time and help. Last but not least, I thank all of my friends and family for always being there whenever I need them." @default.
- W122103775 created "2016-06-24" @default.
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- W122103775 date "2012-01-06" @default.
- W122103775 modified "2023-09-26" @default.
- W122103775 title "Polynomial Chaos Expansions for Random Ordinary Differential Equations" @default.
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