Listar MAT_Articles por autoría "3f3662fe-33c2-4cc2-b68a-ffab76ac2722"
Mostrando ítems 1-17 de 17
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A full probabilistic solution of the random linear fractional differential equation via the random variable transformation technique
Burgos Simón, Clara; Calatayud, Julia; Cortés, Juan Carlos; Navarro-Quiles, A. John Wiley & Sons, Ltd. (2018-11-28)This paper provides a full probabilistic solution of the randomized fractionallinear nonhomogeneous differential equation with a random initial conditionvia the computation of the first probability density function of the ... -
A modified perturbation method for mathematical models with randomness: An analysis through the steady-state solution to Burgers’ PDE
Calatayud, Julia; Cortés, Juan Carlos; Jornet, Marc John Wiley and Sons (2020-04-12)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 cannot ... -
Analysis of the random heat equation via approximate density functions
Calatayud, Julia; Cortés, Juan Carlos Editura Academiei Romane (2021)In this paper we study the randomized heat equation with homo- geneous boundary conditions. The diffusion coefficient is assumed to be a random variable and the initial condition is treated as a stochastic process. The ... -
Una aplicación del teorema del valor medio para estudiar series numéricas
Burgos, Clara; Calatayud, Julia; Cortés, Juan Carlos; Jornet, Marc Una aplicación del teorema del valor medio para estudiar series numéricas (2021-10)In this note we show an application of the mean value theorem to derive the convergence/divergence of numerical series. In particular, our analysis allows us to derive the convergence of p-series and to derive the classical ... -
Computational uncertainty quantification for random non-autonomous second order linear differential equations via adapted gPC: a comparative case study with random Fröbenius method and Monte Carlo simulation
Calatayud, Julia; Cortés, Juan Carlos; Jornet, Marc De Gruyter (2018-12)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 equations, ... -
Computational uncertainty quantification for random time‐discrete epidemiological models using adaptive gPC
Calatayud, Julia; Cortés, Juan Carlos; Jornet, Marc; Villanueva, Rafael-Jacinto John Wiley & Sons, Ltd. (2018-10-22)Population dynamics models consisting of nonlinear difference equations allow us to get a better understanding of theprocesses involved in epidemiology. Usually, these mathematical models are studied under a deterministic ... -
Dealing with variability in ecological modelling: An analysis of a random non-autonomous logistic population model
Calatayud, Julia; Cortés, Juan Carlos; Dorini, Fabio Antonio; Jornet, Marc John Wiley & Sons, Ltd. (2021-05-09)This paper presents a methodology to deal with the randomness associated toecological modelling. Data variability makes it necessary to analyse the impactof random perturbations on the fitted model parameters. We conduct ... -
Improving the Approximation of the First- and Second-Order Statistics of the Response Stochastic Process to the Random Legendre Differential Equation
Calatayud, Julia; Cortés, Juan Carlos; Jornet, Marc Springer Nature Switzerland AG (2019-04-16)In this paper, we deal with uncertainty quantification for the random Legendre differential equation, with input coefficient A and initial conditions X0 and X1. In a previous study (Calbo et al. in Comput Math Appl ... -
Improving the approximation of the probability density function of random nonautonomous logistic-type differential equations
Calatayud, Julia; Cortés, Juan Carlos; Jornet, Marc John Wiley & Sons, Ltd. (2019-08-16)In this paper, we address the problem of approximating the probability density function of the following random logistic differential equation: P ′ (t, 𝜔�) = A(t, 𝜔�)(1 − P(t, 𝜔�))P(t, 𝜔�), t ∈ [t0, T], P(t0, 𝜔�) ... -
Lp-calculus Approach to the Random Autonomous Linear Differential Equation with Discrete Delay
Calatayud, Julia; Cortés, Juan Carlos; Jornet, Marc Springer Nature Switzerland AG (2019-06-19)In this paper, we provide a full probabilistic study of the random autonomous linear differential equation with discrete delay τ > 0: x (t) = ax(t) + bx(t − τ ), t ≥ 0, with initial condition x(t) = g(t), −τ ≤ t ≤ 0. ... -
On the convergence of adaptive gPC for non-linear random difference equations: Theoretical analysis and some practical recommendations
Calatayud, Julia; Cortés, Juan Carlos; Jornet, Marc International Scientific Research Publications (2018-06-19)In this paper, the application of adaptive generalized polynomial chaos (gPC) to quantify the uncertainty for non-linear random difference equations is analyzed. It is proved in detail that, under certain assumptions, the ... -
On the random wave equation within the mean square context
Calatayud, Julia; Cortés, Juan Carlos; Jornet, Marc American Institute of Mathematical Sciences (AIMS) (2022-02)This paper deals with the random wave equation on a bounded domain with Dirichlet boundary conditions. Randomness arises from the velocity wave, which is a positive random variable, and the two initial conditions, which ... -
Random non-autonomous second order linear differential equations: mean square analytic solutions and their statistical properties
Calatayud, Julia; Cortés, Juan Carlos; Jornet, Marc; Villafuerte, L. Springer (2018-10-24)In this paper we study random non-autonomous second order linear differential equations by taking advantage of the powerful theory of random difference equations. The coefficients are assumed to be stochastic processes, ... -
Solving a class of random non-autonomous linear fractional differential equations by means of a generalized mean square convergent power series
Burgos Simón, Clara; Calatayud, Julia; Cortés, Juan Carlos; Villafuerte, L. Elsevier Ltd. (2017-11)The aim of this paper is to solve a class of non-autonomous linear fractional differential equations with random inputs. A mean square convergent series solution is constructed in the case that the fractional order of ... -
Some Notes to Extend the Study on Random Non-Autonomous Second Order Linear Differential Equations Appearing in Mathematical Modeling
Calatayud, Julia; Cortés, Juan Carlos; Jornet, Marc MDPI (2018-11-27)The objective of this paper is to complete certain issues from our recent contribution (Calatayud, J.; Cortés, J.-C.; Jornet, M.; Villafuerte, L. Random non-autonomous second order linear differential equations: mean ... -
The damped pendulum random differential equation: A comprehensive stochastic analysis via the computation of the probability density function
Calatayud, Julia; Cortés, Juan Carlos; Jornet, Marc Elsevier B.V. (2018-08-13)This paper deals with the damped pendulum random differential equation: X¨(t)+2ω0ξX˙(t) + ω 2 0 X(t) = Y(t), t ∈ [0, T ], with initial conditions X(0) = X0 and X˙(0) = X1. The forcing term Y(t) is a stochastic process ... -
Uncertainty quantification for random parabolic equations with nonhomogeneous boundary conditions on a bounded domain via the approximation of the probability density function
Calatayud, Julia; Cortés, Juan Carlos; Jornet, Marc John Wiley & Sons, Ltd. (2018-11-14)This paper deals with the randomized heat equation defined on a general bounded interval [L1, L2] and with nonhomogeneous boundary conditions. The solution is a stochastic process that can be related, via changes of variable, ...