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Boundary Summation Equation Preconditioning for Ordinary Differential Equations with Constant Coefficients on Locally Refined Meshes
Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
2012 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

This thesis deals with the numerical solution of ordinary differential equations (ODEs) using finite difference (FD) methods. In particular, boundary summation equation (BSE) preconditioning for FD approximations for ODEs with constant coefficients on locally refined meshes is studied. Firstly, the BSE for FD approximations of ODEs with constant coefficients is derived on a locally refined mesh. Secondly, the obtained linear system of equations are solved by the iterative method GMRES. Then, the arithmetic complexity and convergence rate of the iterative solution of the BSE formulation are discussed. Finally, numerical experiments are performed to compare the new approach with the FD approach. The results show that the BSE formulation has low arithmetic complexity and the convergence rate of the iterative solvers is fast and independent of the number of grid points.

Place, publisher, year, edition, pages
2012. , 57 p.
Keyword [en]
Ordinary differential equations, constant coefficients, finite difference, boundary summation equation, GMRES, convergence rate.
National Category
Computational Mathematics
URN: urn:nbn:se:liu:diva-102573ISRN: LiTH-MAT-EX-2012/09-SEOAI: diva2:679593
Subject / course
Available from: 2014-01-15 Created: 2013-12-14 Last updated: 2014-01-15Bibliographically approved

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Guzainuer, Maimaitiyiming
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