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Some notes to extend the study on random non-autonomous second order linear differential equations appearing in Mathematical Modeling

Autor: Calatayud, J., Cortés, J. -C., Jornet, M.

The objective of this paper is to complete certain issues from our recent contribution [J. Calatayud, J.-C. Cort\'es, M. Jornet, L. Villafuerte, Random non-autonomous second order linear differential equations: mean square analytic solutions and thei

Externí odkaz: http://arxiv.org/abs/1811.07887

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Improving the approximation of the first and second order statistics of the response process to the random Legendre differential equation

Autor: Calatayud, J., Cortés, J. -C., Jornet, M.

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 G. et al, Comput. Math. Appl., 61(9), 2782--2792 (2011

Externí odkaz: http://arxiv.org/abs/1807.03141

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Approximation of the probability density function of the randomized heat equation with non-homogeneous boundary conditions

Autor: Calatayud, J., Cortés, J. C., Jornet, M.

This paper deals with the randomized heat equation defined on a general bounded interval $[L_1,L_2]$ and with non-homogeneous boundary conditions. The solution is a stochastic process that can be related, via changes of variable, with the solution st

Externí odkaz: http://arxiv.org/abs/1805.03738

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On the approximation of the probability density function of the randomized non-autonomous complete linear differential equation

Autor: Catatayud, J., Cortes, J. -C., Jornet, M.

In this paper we study the randomized non-autonomous complete linear differential equation. The diffusion coefficient and the source term in the differential equation are assumed to be stochastic processes and the initial condition is treated as a ra

Externí odkaz: http://arxiv.org/abs/1802.04188

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On the approximation of the probability density function of the randomized heat equation

Autor: Calatayud, J., Cortes, J. -C., Jornet, M.

In this paper we study the randomized heat equation with homogeneous boundary conditions. The diffusion coeffcient is assumed to be a random variable and the initial condition is treated as a stochastic process. The solution of this randomized partia

Externí odkaz: http://arxiv.org/abs/1802.04190

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