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Series Representation of Flux for the Boussinesq Equation
Author(s) -
Tolikas P.,
Damaskinidou A.,
Sidiropoulos E.
Publication year - 1990
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr026i012p02881
Subject(s) - mathematics , mathematical analysis , boundary value problem , perturbation (astronomy) , ordinary differential equation , nonlinear system , series (stratigraphy) , partial differential equation , variable (mathematics) , differential equation , dirichlet boundary condition , physics , geology , paleontology , quantum mechanics
The Boussinesq equation, supplemented with Dirichlet‐type boundary conditions, is used to describe one‐dimensional groundwater flow. After a number of transformations a nonlinear ordinary differential equation is obtained with flux as the dependent variable. Through perturbation the slope of the water profile at the origin is expressed in the form of a rapidly converging series and can, therefore, be calculated to the desired accuracy. Thus, the corresponding two‐point boundary problem is solved without iteration. Also, quantities related to physical aspects of the problem are easily calculated. Furthermore, the same treatment is directly applicable to a number of other physical and engineering situations governed by the same equations.