An application of the decomposition method to the matrix Riccati equation in a neutron transport process
type: Item
instance of: scholarly article
title: An application of the decomposition method to the matrix Riccati equation in a neutron transport process
zbMATH Open document ID: 0673.34007
DOI: 10.1016/0022-247X(88)90104-7
author: S. H. Smith
published in: Journal of Mathematical Analysis and Applications
publication date: 1988-01-01T00:00:00Z
review text: The differential matrix Riccati equation \[ R'(x)=B(x)+D(x)R(x)+R(x)D(x)+R(x)B(x)R(x) \] subject to the initial condition \(R(0)=0\), where B(x), D(x) are continuous non-negative \(n\times n\) matrix valued functions, is considered. The Adomian decomposition method is applied to give an analytical approximation of the solution which is searched in the form \(\Phi =\sum^{m}_{k=0}R_ k\) with \[ R_ 0=L^{-1}B,\quad R_ k=L^{-1}\{DR_{k-1}+R_{k-1}D\}+L^{- 1}\{\sum^{k-1}_{i=0}R_ iBR_{\quad k-i}\},\quad k\geq 1, \] where \(L^{-1}=\int^{x}_{0}[.]ds.\) To show the accuracy of the method, a model of a neutron steady-state transport process is proposed, which allows to evaluate the matrix coefficient functions in a rather simple way. Different order approximations of the solution are obtained and compared with the direct numerical integration of the equation.
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 34A25
zbMATH DE Number: 4101611
zbMATH Keywords: differential matrix Riccati equation
zbMATH Keywords: Adomian decomposition method
zbMATH Keywords: neutron steady-state transport process
zbMATH Keywords: numerical integration
reviewed by: L. M. Berkovich
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4101611