Semi-implicit spectral deferred correction methods for ordinary differential equations
Semi-implicit spectral deferred correction methods for ordinary differential equations
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DOI：
10.4310/cms.2003.v1.n3.a6
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发表时间：
2003-09
影响因子：
1
通讯作者：
M. Minion
中科院分区：
文献类型：
--
作者：
M. Minion
提出了一种半隐式的谱延迟校正方法（SISDC），用于求解同时具有刚性和非刚性项的常微分方程。对Dutt、Greengard和Rokhlin关于积分点的选择和校正迭代的形式的原始光谱延迟校正方法进行了几次修改和变化。所得到的ODE方法的稳定性和准确性进行了探讨分析和数值。SISDC方法旨在与线方法相结合，以产生一个灵活的框架，用于创建偏微分方程的高阶半隐式方法。讨论和数值例子的SISDC方法应用于对流扩散型方程。结果表明，高阶SISDC方法比半隐式Runge-Kutta方法更有效的中度刚性问题的精度每功能评估。
A semi-implicit formulation of the method of spectral deferred corrections (SISDC) for ordinary differential equations with both stiff and non-stiff terms is presented. Several modifications and variations to the original spectral deferred corrections method by Dutt, Greengard, and Rokhlin concerning the choice of integration points and the form of the correction iteration are presented. The stability and accuracy of the resulting ODE methods are explored analytically and numerically. The SISDC methods are intended to be combined with the method of lines approach to yield a flexible framework for creating higher-order semi-implicit methods for partial differential equations. A discussion and numerical examples of the SISDC method applied to advection-diffusion type equations are included. The results suggest that higher-order SISDC methods are more efficient than semi-implicit Runge-Kutta methods for moderately stiff problems in terms of accuracy per function evaluation.