New contributions to the solution of transport equations in porous media

Authors:
S. E. Serrano;G. Adomian
Affiliations:
Department of Civil Engineering University of Kentucky, Lexington, KY 40506, U.S.A.;General Analytics Corporation 155 Clyde Road, Athens, GA 30605, U.S.A.
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
1996

Citing 2
Cited 1

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The decomposition method and linear partial differential equations

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A series solution of the Cauchy problem for the generalized d-dimensional Schrödinger equation with a power-law nonlinearity

Computers & Mathematics with Applications

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Abstract

In this article recent new developments in the method of decomposition as applied to the general solution of the three-dimensional deterministic/stochastic transport equation in heterogeneous porous media are presented with several applications to convection-dispersion models, spatial scale-dependent and time scale-dependent dispersion equations in heterogeneous porous media, simulation examples with coefficients of variability of up to 500%, and verification with exact solutions. The decomposition method offers fundamental advantages that could be used to build a more realistic theory of groundwater flow and contaminant transport than the current small perturbations theories.