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Analytic-numerical solution of random parabolic models: a mean square fourier transform approach

    María-Consuelo Casabán Affiliation
    ; Juan-Carlos Cortés Affiliation
    ; Lucas Jódar Affiliation

Abstract

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 infinite 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.

Keyword : mean square random calculus, random parabolic models, analytic-numerical solution, random mean square quadrature formulae, random Fourier transform

How to Cite
Casabán, M.-C., Cortés, J.-C., & Jódar, L. (2018). Analytic-numerical solution of random parabolic models: a mean square fourier transform approach. Mathematical Modelling and Analysis, 23(1), 79-100. https://doi.org/10.3846/mma.2018.006
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Feb 20, 2018
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