On the spectral deferred correction of splitting methods for initial value problems
On the spectral deferred correction of splitting methods for initial value problems
复制标题
初值问题分裂法的谱延迟修正
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
R. Zhou
中科院分区：
文献类型：
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作者：
T. Hagstrom;R. Zhou
谱延迟校正是一种使用低阶方法作为基本方案构建高阶、刚性稳定时间积分器的灵活技术。在这里，我们研究它们与分裂方法结合使用来解决偏微分方程的初始边值问题。我们利用它们与隐式龙格-库塔方法的密切联系来证明可以达到基本求积规则的完全精度。我们还通过实验检查了平流扩散和反应扩散方程的各种分裂方法的稳定性。
Spectral deferred correction is a flexible technique for constructing high-order, stiffly-stable time integrators using a low order method as a base scheme. Here we examine their use in conjunction with splitting methods to solve initial-boundary value problems for partial differential equations. We exploit their close connection with implicit Runge–Kutta methods to prove that up to the full accuracy of the underlying quadrature rule is attainable. We also examine experimentally the stability properties of the methods for various splittings of advection-diffusion and reaction-diffusion equations.