An iterative method based on equation decomposition for the fourth‐order singular perturbation problem | Zendy

Han Houde | Zendy; Huang Zhongyi | Zendy; Zhang Shangyou | Zendy

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An iterative method based on equation decomposition for the fourth‐order singular perturbation problem

Author(s) -

Han Houde,

Huang Zhongyi,

Zhang Shangyou

Publication year - 2013

Publication title -

numerical methods for partial differential equations

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.901

H-Index - 61

eISSN - 1098-2426

pISSN - 0749-159X

DOI - 10.1002/num.21740

Subject(s) - mathematics , singular perturbation , perturbation (astronomy) , domain decomposition methods , partial differential equation , boundary value problem , iterative method , mathematical analysis , singular solution , rate of convergence , elliptic partial differential equation , mathematical optimization , finite element method , computer science , channel (broadcasting) , computer network , physics , quantum mechanics , thermodynamics

In this article, we propose an iterative method based on the equation decomposition technique (1) 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 < ε ≪ 1, and the convergence rate is very fast. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013

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