PB2: Contributed Session

Room: Old Main Academic Center 3050

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Chair: Mohammad Sepehrifar,  Mississippi State University

Stefano Di Giovacchino, University of L'Aquila

Time: 2:40 pm - 3:00 pm (CST)

Title: Numerical mean-square contractivity for stochastic differential equations


In this talk, we address our attention to the analysis of nonlinear stability properties characterizing stochastic v-methods and Runge-Kutta methods applied to mean-square dissipative stochastic differential equations. These properties are established in terms of preservation, along the discretized dynamics, of the same mean-square contractive behavior visible along exact solutions to such problems. Regarding stochastic v-methods, these properties are translated in terms of suitable stepsize restrictions. Concerning stochastic Runge-Kutta methods, we show how this conservation property is inherited along the solutions generated by proper stochastic perturbation of an algebraically stable deterministic Runge-Kutta method. We discover that these properties are given by further restrictions on the coeffcients of the stochastic Runge-Kutta methods. Numerical experiments will be also provided to con rm the theoretical analysis. This is a joint work with Raffaele D'Ambrosio (University of L'Aquila).

Ghodsieh Ghanbari, Mississippi State University

Time:  3:00 pm - 3:20 pm (CST)

Title: A numerical approach for solving time delay fractional-order optimal control problems by using fractional-order Chebyshev wavelets


A novel numerical method based on generalized fractional-order Chebyshev wavelets is presented for the time delay fractional optimal control problems. We construct a formula for calculating the exact value of the Riemann-Liouville fractional integral operator of the generalized fractional-order Chebyshev wavelets by using the incomplete beta function. Several examples are considered. Our numerical results are compared with the other results presented in the literature.

Kobra Rabiei, Mississippi State University 

Time:  3:40 pm - 4:00 pm (CST)

Title: An efficient method to solve the fractional pantograph differential equations using the hybrid of Boubaker polynomials and block-pulse functions


This paper aims to provide a novel numerical method for solving the fractional pantograph differential equations. The method is constructed using the hybrid of Boubaker polynomials and block-pulse functions (HBPBP). By applying the regularized beta function, an exact formula for computing the Riemann-Liouville fractional integral operator of the HBPBP is provided. The given exact formula and the properties of HBPBP are used to reduce the given fractional pantograph differential equation to a system of algebraic equations. The method is easy to implement and provides very accurate solutions. Several examples are given to show the applicability and effectiveness of the method.

Godlove Appiah,  Mississippi State University

Time:  4:00 pm - 4:20 pm (CST)

Title: Computational method of testing shape parameter (β) of the power-law process with applications to reliability system engineering 


As most people now live in an era of extreme reliance on multiple technologies and sophisticated systems to store and manage sensitive information, researchers are constantly urged to obtain and improve measurements, methodologies, and models that have the ability to evaluate systems reliability, security, and dependability. The objective of the present article is to develop a non-parametric hypothesis testing procedure to statistically test the shape parameter (β) of the Power-Law Process (PLP), also known as the Non-Homogeneous Poisson Process (NHPP). The non-parametric test procedure is constructed using a two-stage U-statistics (TU-statistics) method to test if the system’s reliability is improving over time (β < 1). Furthermore, we compare the results of the TU-statistics with results obtained using incomplete U-statistics. This comparison is made using simulated reliability data sets from the Power-Law Process, Weibull, and Lognormal distributions. In all three scenarios, the TU-statistics performs better than the incomplete Ustatistics in terms of the probability of the testing procedure correctly rejecting the null hypothesis. In the context of repairable system reliability, we demonstrate that reliability improves using this method on realized missing failure data from the system simulated and real-world data.

(Joint work with Mohammad Sepehrifar)

Tobias Oketch, Mississippi State University

Time:  4:20 pm - 4:40 pm (CST)

Title: Computational Methods for Selecting Priors and Posterior Uncertainty for Single Failure Mode Systems


A complex power law process may generate an unusual distribution of failure data that classical modeling schemes may not fit properly to reveal the special features (extreme values and curvatures) of the distribution of interest. In this research, we study a Markov Chain Monte Carlo process based on the Hamiltonian Dynamics that sequentially samples the spaces of parameters of a power-law process. Simulate systems’ life data, and integrate different sets of prior distributions of the power-law process to determine precise parameter candidates for posterior predictive models that best characterize the system’s life cycle. We generalize choices of the improper priors and those from the exponential family of distributions.

(Joint work with Mohammad Sepehrifar)