Adaptive decomposition finite difference methods for solving singular problems -- a review
type: Item
instance of: scholarly article
title: Adaptive decomposition finite difference methods for solving singular problems -- a review
zbMATH Open document ID: 1180.35003
author: Qin Sheng
published in: Frontiers of Mathematics in China
publication date: 2009-11-09T00:00:00Z
review text: This survey article presents the latest developments in the field of adaptive decomposition finite difference methods for solving singular problems. The first part of it presents a history of this type of methods that can be traced back to the early fifties. Section 2 is concerned with the basic theory of decomposition methods and approximations with a precise description regarding basic splitting. Section 3 of the paper focuses on adaptive decomposition methods for solving nonlinear reaction-diffusion equations with quenching combustion type nonlinearities. Here the monotonicity of the sequential numerical solutions generated from decomposition procedure is proved. Section 4 is devoted to investigations of solitary wave problems governed by sine-Gordon equation. Locally linearized stability analysis is studied for the variable step decomposed finite difference methods. Various numerical experiments are presented. Finally, last section summarizes the whole presentation and presents some expectations for the forthcoming researches in the field.
reviewed by: Marius Ghergu
Mathematics Subject Classification ID: 35-02
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 65N50
Mathematics Subject Classification ID: 65D25
Mathematics Subject Classification ID: 65D30
zbMATH DE Number: 5627219
zbMATH Keywords: uniform and nonuniform grid
zbMATH Keywords: monotonicity and stability
zbMATH Keywords: quenching combustion type nonlinearities
MaRDI profile type: Publication
full work available at URL: s11464-009-0038-0
OpenAlex ID: W2016060593
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DOI: 10.1007/S11464-009-0038-0
description: scientific article; zbMATH DE number 5627219