Solving initial and two-point boundary value linear random differential equations: A mean square approach

Cortés, Juan; Jódar, Lucas; Roselló, María Dolores; Villafuerte, L.

doi:10.1016/j.amc.2012.08.066

Cited by 13 publications

References 7 publications

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“…. The cases p = 2 and p = 4, corresponding to the so called mean square and mean fourth convergence, respectively, play a major role in the study of random differential equations [10,30]. This key role will also be manifested throughout this paper as well.…”

Section: Preliminariesmentioning

confidence: 92%

See 1 more Smart Citation

Analytic-Numerical Solution of Random Parabolic Models: A Mean Square Fourier Transform Approach

Casabán¹,

Cortés²,

Jódar³

2018

Mathematical Modelling and Analysis

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This paper deals with the construction of mean square analytic-numerical solution of parabolic partial differential problems where both initial condition and coefficients are stochastic processes. By using a random Fourier transform, an inf- nite integral form of the solution stochastic process is firstly obtained. Afterwards, explicit expressions for the expectation and standard deviation of the solution are obtained. Since these expressions depend upon random improper integrals, which are not computable in an exact manner, random Gauss-Hermite quadrature formulae are introduced throughout an illustrative example.

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Section: Preliminariesmentioning

confidence: 92%

“…a(t) is • 4,RV -continuous. Then, Theorem 8 of [10] allows us to guarantee that the mean square solution s.p. of the IVP (3.9) is given by…”

Section: Approximation Of Random Improper Integrals By the Random Gaumentioning

confidence: 99%

Analytic-Numerical Solution of Random Parabolic Models: A Mean Square Fourier Transform Approach

Casabán¹,

Cortés²,

Jódar³

2018

Mathematical Modelling and Analysis

View full text Add to dashboard Buy / Rent full text

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“…In this paper, we introduce the random Fourier sine and cosine transforms and their mean square operational calculus to solve random temperature distribution in a semi-infinite bar with random temperature or random heat flow at one end. Using results about random ordinary differential equations of [6] allows us to find closed-form solutions stochastic process (s.p.) of random heat problems as in the deterministic case.…”

Section: Introductionmentioning

confidence: 99%

Analytic-Numerical Solution of Random Boundary Value Heat Problems in a Semi-Infinite Bar

Casabán

Cortés²,

García-Mora³

et al. 2013

Abstract and Applied Analysis

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This paper deals with the analytic-numerical solution of random heat problems for the temperature distribution in a semi-infinite bar with different boundary value conditions. We apply a random Fourier sine and cosine transform mean square approach. Random operational mean square calculus is developed for the introduced transforms. Using previous results about random ordinary differential equations, a closed form solution stochastic process is firstly obtained. Then, expectation and variance are computed. Illustrative numerical examples are included.

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“…Currently, they are exerting a profound influence on the analysis of many problems in engineering and science [10,11]. Most of these contributions are based on mean square calculus [8,[12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Random First-Order Linear Discrete Models and Their Probabilistic Solution: A Comprehensive Study

Casabán

Cortés

Romero

et al. 2016

Abstract and Applied Analysis

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This paper presents a complete stochastic solution represented by the first probability density function for random first-order linear difference equations. The study is based on Random Variable Transformation method. The obtained results are given in terms of the probability density functions of the data, namely, initial condition, forcing term, and diffusion coefficient. To conduct the study, all possible cases regarding statistical dependence of the random input parameters are considered. A complete collection of illustrative examples covering all the possible scenarios is provided.

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Solving initial and two-point boundary value linear random differential equations: A mean square approach

Cited by 13 publications

References 7 publications

Analytic-Numerical Solution of Random Parabolic Models: A Mean Square Fourier Transform Approach

Analytic-Numerical Solution of Random Parabolic Models: A Mean Square Fourier Transform Approach

Analytic-Numerical Solution of Random Boundary Value Heat Problems in a Semi-Infinite Bar

Random First-Order Linear Discrete Models and Their Probabilistic Solution: A Comprehensive Study

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