Abstract
This papers introduces a procedure for solving a non-linear system of partial differential equations of the parabolic type with random coefficients. An adaptive method transforms the system into a set of ordinary differential equations which is solved after a suitable expansion of the probability density of the unknown random field in terms of orthogonal polynomials.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Adomian G., Stochastic Systems, Academic Press, New York, 1983.
Soong T.T., RandomDifferential Equations in Science and Engineering, Academic Press, New York, 1973.
Carlomusto L., Pianese A. and deSocio L.M., “Heat Transfer for the Two Phases of a Porous Storage Matrix”, in Energy Storage Systems(Kilkis B. and Kakac S.eds.), pp. 721–728, Kluwer Ac. Publ., The Netherlands, 1989.
Bonzani I., Riganti R., “On the Probability Density of Random Fields in Continuum Mechanics”, Stochastic Analysis Appl., 1, pp. 1–18, 1989.
Bellomo N., deSocio L.M. and Monaco R., “Random Heat Equation: Solutions by the Stochastic Adaptive Interpolation Method”, Comp. Math. Appl., 16, pp. 759–766, 1988.
Bellomo N., Flandoli F., “Stochastic Partial Differential Equations in Continuum Physics: on the Foundations of the Stochastic Adaptive Interpolation Method for Ito’s Type Equations”, Math. Comp. Simul., 2nd special issue on Stochastic Systems Modelling, (to appear).
Carlomusto L., deSocio L.M., Gaffuri G., and Pianese A., “An Efficient Method for Solving the Boundary Layer Equations”, Proc. 5th Int. Conf. on Boundary and Interior Layers — computational and Asymptotic Methods, BAIL V, pp. 103–108, 1988, Shanghai, China.
Bellman R., Adomian G., Partial Differential Equations, Reidel, New York, 1985.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Computational Mechanics Publications
About this chapter
Cite this chapter
Carlomusto, L., Pianese, A., de Socio, L.M. (1991). A Method for Solving the Diffusion Equation with Random Coefficients. In: Spanos, P.D., Brebbia, C.A. (eds) Computational Stochastic Mechanics. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3692-1_28
Download citation
DOI: https://doi.org/10.1007/978-94-011-3692-1_28
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-85166-698-0
Online ISBN: 978-94-011-3692-1
eBook Packages: Springer Book Archive