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

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Abstract

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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