NDLI: High-Order Convergence of Spectral Deferred Correction Methods on General Quadrature Nodes

Content Provider	Springer Nature Link
Author	Tang, Tao Xie, Hehu Yin, Xiaobo
Copyright Year	2012
Abstract	It has been demonstrated that spectral deferred correction (SDC) methods can achieve arbitrary high order accuracy and possess good stability properties. There have been some recent interests in using high-order Runge-Kutta methods in the prediction and correction steps in the SDC methods, and higher order rate of convergence is obtained provided that the quadrature nodes are uniform. The assumption of the use of uniform mesh has a serious practical drawback as the well-known Runge phenomenon may prevent the use of reasonably large number of quadrature nodes. In this work, we propose a modified SDC methods with high-order integrators which can yield higher convergence rates on both uniform and non-uniform quadrature nodes. The expected high-order of accuracy is theoretically verified and numerically demonstrated.
Starting Page	1
Ending Page	13
Page Count	13
File Format	PDF
ISSN	08857474
Journal	Journal of Scientific Computing
Volume Number	56
Issue Number	1
e-ISSN	15737691
Language	English
Publisher	Springer US
Publisher Date	2012-10-25
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Spectral deferred correction (SDC) Modified SDC High-order convergence General quadrature nodes Algorithms Computational Mathematics and Numerical Analysis ApplicationMathematics/Computational Methods of Engineering Theoretical, Mathematical and Computational Physics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Theoretical Computer Science Engineering Computational Theory and Mathematics Computational Mathematics Numerical Analysis Software

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