High-Order Convergence of Spectral Deferred Correction Methods on General Quadrature Nodes
High-Order Convergence of Spectral Deferred Correction Methods on General Quadrature Nodes
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DOI：
10.1007/s10915-012-9657-9
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发表时间：
2013-07
影响因子：
2.5
通讯作者：
T. Tang;Hehu Xie;Xiaobo Yin
中科院分区：
文献类型：
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作者：
T. Tang;Hehu Xie;Xiaobo Yin
事实证明，谱延迟校正（SDC）方法可以达到任意高阶精度并具有良好的稳定性。近年来，在SDC方法的预测和校正步骤中使用高阶Runge-Kutta方法引起了人们的兴趣，只要求积节点是均匀的，就可以获得更高的收敛速度。使用均匀网格的假设具有严重的实际缺点，因为众所周知的龙格现象可能会阻止使用相当大数量的正交节点。本文提出了一种改进的高阶积分SDC方法，该方法在均匀和非均匀积分点上都具有更高的收敛速度。理论上验证和数值模拟表明，预期的高阶精度。
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 areuniform. 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 onbothuniform and non-uniform quadrature nodes. The expected high-order of accuracy is theoretically verified and numerically demonstrated.