Search results for "Random differential equation"
showing 3 items of 3 documents
Constructing adaptive generalized polynomial chaos method to measure the uncertainty in continuous models: A computational approach
2015
Due to errors in measurements and inherent variability in the quantities of interest, models based on random differential equations give more realistic results than their deterministic counterpart. The generalized polynomial chaos (gPC) is a powerful technique used to approximate the solution of these equations when the random inputs follow standard probability distributions. But in many cases these random inputs do not have a standard probability distribution. In this paper, we present a step-by-step constructive methodology to implement directly a useful version of adaptive gPC for arbitrary distributions, extending the applicability of the gPC. The paper mainly focuses on the computation…
Some notes on a second-order random boundary value problem
2017
We consider a two-point boundary value problem of second-order random differential equation. Using a variant of the α-ψ-contractive type mapping theorem in metric spaces, we show the existence of at least one solution.
SOLUTION TO RANDOM DIFFERENTIAL EQUATIONS WITH BOUNDARY CONDITIONS
2017
We study a family of random differential equations with boundary conditions. Using a random fixed point theorem, we prove an existence theorem that yields a unique random solution.