[EN] This paper provides a full probabilistic solution of the randomized fractional linear nonhomogeneous differential equation with a random initial condition via the computation of the first probability density function ...
[EN] The variability of the data and the incomplete knowledge of the true physics require the incorporation of randomness into the formulation of mathematical models. In this setting, the deterministic numerical methods ...
Calatayud Gregori, Julia; Cortés López, Juan Carlos; Jornet Sanz, Marc; Villanueva Micó, Rafael Jacinto(Editorial Universitat Politècnica de València, 2019-10-01)
This book is aimed at covering the bases on random variables, random vectors and stochastic processes, necessary to be able to address the study of stochastic models based mainly on random and stochastic differential ...
Calatayud, Julia; Cortés, J.-C.(Editura Academiei Romane, 2021)
[EN] In this paper we study the randomized heat equation with homogeneous boundary conditions. The diffusion coefficient is assumed to be a random
variable and the initial condition is treated as a stochastic process. The ...
Calatayud-Gregori, Julia; Cortés, J.-C.; Jornet-Sanz, Marc(Texas State University. Department of Mathematics, 2019-07-16)
[EN] Solving a random differential equation means to obtain an exact or approximate expression for the solution stochastic process, and to compute its statistical properties, mainly the mean and the variance functions. ...
[EN] In this work, we study the full randomized versions of Airy, Hermite and Laguerre differential equations, which depend on a random variable appearing as an equation coefficient as well as two random initial conditions. ...
[EN] In this paper, we deal with computational uncertainty quantification for stochastic models with one random input parameter. The goal of the paper is twofold: First, to approximate the set of probability density functions ...
Calatayud Gregori, Julia(Universitat Politècnica de València, 2020-03-05)
[EN] Mathematical models based on deterministic differential equations do not take into account the inherent uncertainty of the physical phenomenon (in a wide sense) under study. In addition, inaccuracies in the collected ...
[EN] This paper presents a methodology to quantify computationally the uncertainty in a class of differential equations often met in Mathematical Physics, namely random non-autonomous second-order linear differential ...
Calatayud-Gregori, Julia; Cortés, J.-C.; Jornet-Sanz, Marc; Villanueva Micó, Rafael Jacinto(John Wiley & Sons, 2018)
[EN] Population dynamics models consisting of nonlinear difference equations allow us to get a better understanding of the processes involved in epidemiology. Usually, these mathematical models are studied under a deterministic ...
[EN] This paper concerns the computation of the probability density function of the stochastic solution to general complex systems with uncertainties formulated via random differential equations. In the existing literature, ...
[EN] We study the random heat partial differential equation on a bounded domain assuming that the diffusion coefficient and the boundary conditions are random variables, and the initial condition is a stochastic process. ...
[EN] A computational approach to approximate the probability density function of random differential equations is based on transformation of random variables and finite difference schemes. The theoretical analysis of this ...
Calatayud, J.; Cortés, J.-C.; Dorini, F. A.; Jornet, M.(Elsevier, 2020-06)
[EN] In this paper we extend the study on the linear advection equation with independent stochastic velocity and initial condition performed in Dorini and Cunha (2011). By using both existing and novel results on the ...
[EN] The time evolution of microorganisms, such as bacteria, is of great interest in biology. In the article by D. Stanescu et al. [Electronic Transactions on Numerical Analysis, 34, 44-58 (2009)], a logistic model was ...
[EN] In this paper, we deal with uncertainty quantification for the random Legendre differential equation, with input coefficient A and initial conditions X-0 and X-1. In a previous study (Calbo et al. in Comput Math Appl ...
[EN] In this paper, we address the problem of approximating the probability density function of the following random logistic differential equation: P-'(t,omega)=A(t,omega)(1-P(t,omega))P(t,omega), t is an element of[t(0),T], ...
[EN] In this paper, we provide a full probabilistic study of the random autonomous linear differential equation with discrete delay , with initial condition x(t)=g(t), -t0. The coefficients a and b are assumed to be random ...
Calatayud, Julia; Caraballo, Tomás; Cortés, J.-C.; Jornet, Marc(Texas State University. Department of Mathematics, 2020-05-26)
[EN] In this article we analyze the randomized non-autonomous Bertalanffy model
x' (t, omega) = a(t, omega)x(t, omega) b(t, omega)x(t, omega)(2/3), x(t(0), omega) = x(0)(omega),
where a(t, omega) and b(t, omega) are ...
[EN] In this paper, we are concerned with the construction of numerical schemes for linear random differential equations with discrete delay. For the linear deterministic differential equation with discrete delay, a recent ...