Approximate analytical solution of the nonlinear Bethe equation
type: Item
instance of: scholarly article
title: Approximate analytical solution of the nonlinear Bethe equation
zbMATH Open document ID: 1422.34097
author: O. González-Gaxiola
author: A. León-Ramírez
author: Guillermo Chacón-Acosta
published in: International Journal of Applied and Computational Mathematics
publication date: 2019-04-18T00:00:00Z
review text: 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 of the kinetic energy with \(u \geq 1 \), and \(x\) is a dimensionless measure of the distance pernetrated by the particle into the medium. The LADM has been applied to this method by considering \(\frac{d}{dx}\) as the linear operator \(L_x\) and the nonlinear operator \(Nu=\frac{ln(u+1)}{u}\). They have worked out several examples and proved the accuracy of the solution of the Bethe equation obtained through LADM.
Mathematics Subject Classification ID: 34A45
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 7046074
zbMATH Keywords: Bethe equation
zbMATH Keywords: stopping power
zbMATH Keywords: nonlinear equations
zbMATH Keywords: analytical approximate solution
zbMATH Keywords: Adomian decomposition method
reviewed by: J. Vasundhara Devi
MaRDI profile type: Publication
full work available at URL: s40819-019-0616-0
OpenAlex ID: W2912407570
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DOI: 10.1007/S40819-019-0616-0
description: scientific article; zbMATH DE number 7046074