# Decomposition method applied to hydrology

S. Guellal (Laboratoire Medimat, Université Pierre et Marie Curie, Paris Cedex, France and ICES, L’Ecole Universitaire, La Roche sur Yon, France)
Y. Cherruault (Laboratoire Medimat, Université Pierre et Marie Curie, Paris Cedex, France, and)
M.J. Pujol (Depto de Análisis Mathemático Applicada, Universidad de Alicante, Alicante, Spain)
P. Grimalt (Depto de Análisis Mathemático Applicada, Universidad de Alicante, Alicante, Spain)

ISSN: 0368-492X

Article publication date: 1 June 2000

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## Abstract

In some papers G. Adomian has presented a decomposition technique in order to solve different non‐linear equations. The solution is found as an infinite series quickly converging to accurate solutions. The method is well‐suited for physical problems and it avoids linearization, perturbation and other restrictions, methods and assumptions which may change the problem being solved – sometimes seriously – unnecessarily. Proofs of convergence are given by Cherruault and co‐authors. Many numerical studies for physical phenomena, such as Fisher’s equation, Lorentz’s equation and Edem’s equation are given and solved. In this work, the general equation given by ∂ p \overt = (∇ ⋅(q(x)⋅ ∇p)) + f(x, t) is solved by using decomposition methods, and is compared to other techniques. This equation can be used to describe the motion of a fluid flow in the so‐called reservoir region, where p(x, t) represents the pressure distribution, f(x, t) describes the withdrawal or injection of the fluid, and q(x) is the transmissibility in the reservoir region.

## Citation

Guellal, S., Cherruault, Y., Pujol, M.J. and Grimalt, P. (2000), "Decomposition method applied to hydrology", Kybernetes, Vol. 29 No. 4, pp. 499-504. https://doi.org/10.1108/03684920010322244

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