An iterative method based on equation decomposition for the fourth‐order singular perturbation problem. Issue 3 (30th July 2012)

• Record Type: Journal Article
• Authors: Han, Houde; Huang, Zhongyi; Zhang, Shangyou
• Is Part Of: Numerical methods for partial differential equations. Volume 29:Issue 3(2013:May)
• Page Start: 961
• Page End: 978
• Publication Date: 2012-07-30
• Subjects: Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.21740
• Languages: English
• ISSNs: 0749-159X

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>In this article, we propose an iterative method based on the equation decomposition technique (<xref ref-type="link" rid="bib1">1</xref>) for the numerical solution of a singular perturbation problem of fourth‐order elliptic equation. At each step of the given method, we only need to solve a boundary value problem of second‐order elliptic equation and a second‐order singular perturbation problem. We prove that our approximate solution converges to the exact solution when the domain is a disc. Our numerical examples show the efficiency and accuracy of our method. Our iterative method works very well for singular perturbation problems, that is, the case of 0 &lt; ε ≪ 1, and the convergence rate is very fast. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013</p> </abstract>