The iterative solution of fully implicit discretizations of three-dimensional transport models
type: Item
instance of: scholarly article
title: The iterative solution of fully implicit discretizations of three-dimensional transport models
zbMATH Open document ID: 0890.65099
DOI: 10.1016/S0168-9274(97)00063-9
author: J. Ning
published in: Applied Numerical Mathematics
publication date: 1998-06-23T00:00:00Z
review text: The authors consider systems of spatially three-dimensional weakly coupled advection-diffusion-reaction equations. By spatial difference-discretization (of three-point type in each spatial variable with special upwind modification for the advection terms) they obtain a system of ordinary differential equations for which they discuss in detail a few fully implicit methods of Runge-Kutta type. They investigate some iterative methods of solving the systems of (nonlinear) equations arising at each new time level, with particular emphasis on advantages possible by use of parallel vector computers. Furthermore, they discuss questions of stability of their methods and conclude their paper by displaying results of numerical case studies.
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65L06
zbMATH DE Number: 1088832
zbMATH Keywords: method of lines
zbMATH Keywords: implicit Runge-Kutta method
zbMATH Keywords: parallel computation
zbMATH Keywords: advection-diffusion-reaction equations
zbMATH Keywords: iterative methods
zbMATH Keywords: systems of nonlinear equations
zbMATH Keywords: stability
zbMATH Keywords: numerical examples
reviewed by: Rudolf Gorenflo
MaRDI profile type: Publication
cites work: Analysis approximate factorization in iteration methods
cites work: Q3994335
cites work: Splitting methods for three-dimensional bio-chemical transport
cites work: Iterated Runge–Kutta Methods on Parallel Computers
cites work: Splitting methods for three-dimensional transport models with interaction terms
cites work: Triangularly Implicit Iteration Methods for ODE-IVP Solvers
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description: scientific article; zbMATH DE number 1088832