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Convergence Analysis of an Iterative Method for Nonlinear Partial Differential Equations
Joint Authors
Chen, Ren-Chuen
Li, Chun-Hsien
Ke, Hung-Yu
Source
Journal of Applied Mathematics
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-09-09
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
We will combine linear successive overrelaxation method with nonlinear monotone iterative scheme to obtain a new iterative method for solving nonlinear equations.
The basic idea of this method joining traditional monotone iterative method (known as the method of lower and upper solutions) which depends essentially on the monotone parameter is that by introducing an acceleration parameter one can construct a sequence to accelerate the convergence.
The resulting increase in the speed of convergence is very dramatic.
Moreover, the sequence can accomplish monotonic convergence behavior in the iterative process when some suitable acceleration parameters are chosen.
Under some suitable assumptions in aspect of the nonlinear function and the matrix norm generated from this method, we can prove the boundedness and convergence of the resulting sequences.
Application of the iterative scheme is given to a logistic model problem in ecology, and numerical results for a test problem with known analytical solution are given to demonstrate the accuracy and efficiency of the present method.
American Psychological Association (APA)
Ke, Hung-Yu& Chen, Ren-Chuen& Li, Chun-Hsien. 2013. Convergence Analysis of an Iterative Method for Nonlinear Partial Differential Equations. Journal of Applied Mathematics،Vol. 2013, no. 2013, pp.1-12.
https://search.emarefa.net/detail/BIM-475562
Modern Language Association (MLA)
Ke, Hung-Yu…[et al.]. Convergence Analysis of an Iterative Method for Nonlinear Partial Differential Equations. Journal of Applied Mathematics No. 2013 (2013), pp.1-12.
https://search.emarefa.net/detail/BIM-475562
American Medical Association (AMA)
Ke, Hung-Yu& Chen, Ren-Chuen& Li, Chun-Hsien. Convergence Analysis of an Iterative Method for Nonlinear Partial Differential Equations. Journal of Applied Mathematics. 2013. Vol. 2013, no. 2013, pp.1-12.
https://search.emarefa.net/detail/BIM-475562
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-475562