Results 251 to 260 of about 572,545 (279)

An Approximate Analytical Solution of Richards’ Equation

International Journal of Nonlinear Sciences and Numerical Simulation, 2015
AbstractAn approximate analytical solution of Richards’ equation (RE) in a semi-finite layer of porous medium is obtained in this article. The basic idea is constructing a function between the Boltzmann variableϕand the traveling wave solution of RE, introducing the function into RE and calculating the relevant parameters by differential transform ...
Chen, Xi, Dai, Ying
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Approximate Analytical Solutions for Overland Flows

Water Resources Research, 1990
Following the study of Govindaraju et al. (1988), approximate analytical solutions are presented to the diffusion and kinematic wave models subject to space and time‐varying rainfall. An approximation in the form of the first term of an infinite sine series has been considered. This converts the partial differential equation to an ordinary differential
R. S. Govindaraju, M. L. Kavvas, S. E. Jones   +2 more
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Approximate analytical solution of nucleation problems

Materials Science and Engineering: A, 1993
Abstract A Fokker-Planck-like equation describing the homogeneous nucleation process in one-component system is solved analytically by a novel method based on boundary layer theory combined with a Green function technique. Important characteristics of nucleation (nucleation rate, integrated flux, time lag) are determined. The accuracy of the approach
P Demo, Z Kožíšek
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Approximate Solutions of Analytic Inequality Systems

SIAM Journal on Optimization, 2000
Summary: We consider the stability problem for a system of equalities and inequalities. We prove that when such a system is satisfied approximately at a certain point, it is also satisfied exactly on a nearby point.
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Analytical solution for the AN approximation

Progress in Nuclear Energy, 1997
The aim of this work consists of the presentation of a new derivation and also an analytical solution for the one-dimensional AN approximation of the linear transport equation. Numerical simulations are reported.
Augusto V. Cardona, Marco T.M.B. Vilhena
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Approximate Analytical Solution for Solute Flow During Infiltration and Redistribution

Soil Science Society of America Journal, 1978
Abstract An approximate analytical solution is developed to describe solute flow in soil during infiltration and redistribution. For the solution it is assumed that hydrodynamic dispersion is linearly related to the pore water velocity. In order to use the solution it is necessary to estimate the solute penetration depth.
De Smedt, Florimond, Wierenga, P.J.
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Approximate Analytical Solution of the Nonlinear Bethe Equation

International Journal of Applied and Computational Mathematics, 2019
The authors consider the Bethe equation, which is a nonlinear differential equation, describing the energy loss of electrons when they penetrate a material. They have used the Laplace Adomian decomposition method (LADM) to solve this equation approximated by \[ \frac{du}{dx}+\frac{ln(u+1)}{u}=0,\quad u(0)=u_0, \] where \(u\) is a dimensionless measure ...
O. González-Gaxiola, G. Chacón-Acosta, A. León-Ramírez   +2 more
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Approximate analytic solutions to the NPDD: Short exposure approximations

Optics Communications, 2014
Abstract There have been many attempts to accurately describe the photochemical processes that take places in photopolymer materials. As the models have become more accurate, solving them has become more numerically intensive and more ‘opaque’. Recent models incorporate the major photochemical reactions taking place as well as the diffusion effects ...
Ciara E. Close, John T. Sheridan
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Approximate analytic solutions for nonsimilar boundary layers.

AIAA Journal, 1967
The Crocco equation for zero pressure gradient and a constant viscosity density product is linearized and the results applied to boundary-layer problems where the given initial profile is much different from the Blasius profile. Four linearization assumptions are used, each of which leads to an eigenvalue problem having a discrete spectrum of ...
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Analytical Approximate Solutions for Vasicek Equation

SSRN Electronic Journal, 2007
This paper presents a theoretical analysis for the Vasicek equation in finance. The Adomian decomposition approach is introduced and the analytical solution is obtained. The results reported in this work provide further evidence of the importance of Adomian decomposition in finding the solution of partial differential equation.
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