Analytic-numerical solution of random parabolic models: A mean square Fourier transform approach

[EN] 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.This work has been partially supported by the Spanish Ministerio de Economia y Competitividad grant MTM2013-41765-P.Casabán, M.; Cortés, J.; Jódar Sánchez, LA. (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.2018.0067910023