Analytic-numerical solution of random parabolic models: a mean square fourier transform approach
DOI: https://doi.org/10.3846/mma.2018.006Abstract
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.
Keywords:
mean square random calculus, random parabolic models, analytic-numerical solution, random mean square quadrature formulae, random Fourier transformHow to Cite
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Copyright (c) 2018 The Author(s). Published by Vilnius Gediminas Technical University.
This work is licensed under a Creative Commons Attribution 4.0 International License.
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Copyright (c) 2018 The Author(s). Published by Vilnius Gediminas Technical University.
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This work is licensed under a Creative Commons Attribution 4.0 International License.