Browsing INIT_Articles by Keyword "34F05"
Now showing items 1-8 of 8
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Approximate solutions of randomized non-autonomous complete linear differential equations via probability density functions
Texas State University (2019-07-16)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. However, ... -
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
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, ... -
Improving the Approximation of the First- and Second-Order Statistics of the Response Stochastic Process to the Random Legendre Differential Equation
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
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�) ... -
Random non-autonomous second order linear differential equations: mean square analytic solutions and their statistical properties
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, ... -
Some Notes to Extend the Study on Random Non-Autonomous Second Order Linear Differential Equations Appearing in Mathematical Modeling
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
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
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, ...