The decomposition method and linear partial differential equations

Gabet, Lionel

doi:10.1016/0895-7177(93)90191-z

Cited by 27 publications

(8 citation statements)

References 5 publications

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“…Consider ( The above result indicates that it is always possible to manipulate the simulation time step (i.e., a modeling decision) in order to obtain convergent decomposition series. A rigorous framework for the convergence of decomposition series has also been developed by Gabet [1994Gabet [ , 1993Gabet [ , 1992 …”

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confidence: 99%

Analytical decomposition of the nonlinear unsaturated flow equation

Serrano¹

1998

Water Resources Research

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Applications to the modeling of infiltration subject to hysteresis in the soil-water functional relationships, soil heterogeneity, and time variable point rainfall are also discussed. Other potential applications in water management models under more realistic conditions are possible. The methodology offers advantages over the common smallperturbation solutions: the possibility to study nonstationarity in the random quantities; statistical separability from the physics of the problem (i.e., independence between the system parameters and the input quantities), rather than forced through closure approximations; and the construction of an analytical series solution that converges uniformly to the true nonlinear solution. Finally, because of stability and computational economy with respect to linearized numerical solutions, an analytical solution appears promising.

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confidence: 99%

Analytical decomposition of the nonlinear unsaturated flow equation

Serrano¹

1998

Water Resources Research

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“…A rigorous framework for the convergence of decomposition series has been developed (Gabet 1992(Gabet , 1993(Gabet , 1994 by connecting the method to well known formulations where classical theorems (fixed point theorem, substituted series, etc.) could be used.…”

Section: Analytical Decomposition Methods In Subsurface Contaminant Hmentioning

confidence: 99%

Semigroup and Decomposition Methods in Solving Stochastic Subsurface Contamination Problems

Serrano¹

2002

Stochastic Methods in Subsurface Contaminant Hydrology

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“…With two terms in the series, the solution to the nonlinear problem (5) is Gabet (1993Gabet ( , 1994 and Abbaoui and Cherruault (1994) have shown that when decomposition series converge, they do so very rapidly and only a few terms in the series are required for an accurate solution. Serrano (1998) has shown the rapid convergence of the decomposition series for groundwater flow problems.…”

Section: Analytical Solution To the Stochastic Transient Groundwater mentioning

confidence: 98%