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Erschienen in:
2017 | OriginalPaper | Buchkapitel
On the Behavior of the Error in Numerical Iterative Method for PDE
verfasst von : Toshiyuki Kohno
Erschienen in: Advances in Difference Equations and Discrete Dynamical Systems
Verlag: Springer Singapore
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Abstract
The purpose of paper is to analyze the behavior of the error in the iterative method. Especially, we are interested in the classical iterative method such as SOR method and its preconditioning techniques to solve the linear system \(A{u}={q}\). In order to accelerate convergence, many researchers proposed several preconditioners [4‐8]. There is also preconditioner available for both classical iterative and Krylov subspace methods. We focus on the behavior of error to find a good preconditioner. We treat difference equation derived from partial differential equation(PDE), because the coefficient matrix given by using difference approximation is easy to investigate. By examining the behavior of the error, we choose an effective preconditioner, and show the numerical results.