Abstract Predictor–corrector schemes are designed to be a compromise to retain the stability properties of the implicit schemes and the computational efficiency of the explicit ones. In this paper a complete analytical study for the linear mean-square stability of the two-parameter family of Euler predictor–corrector schemes for scalar stochastic differential equations is given. The analyzed family is given in terms of two parameters that control the degree of implicitness of the method. For each selection of the parameters the stability region is obtained, letting its comparison. Particular cases of the counter-intuitive fact of losing numerical stability by reducing the step size, is confirmed and proved. Figures of the MS-stability regions and numerical examples that confirm the theoretical results are shown.

中文翻译：

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关于随机微分方程的预测器-校正器方案的 MS 稳定性

摘要 预测器-校正器方案旨在保留隐式方案的稳定性特性和显式方案的计算效率的折衷方案。在本文中，给出了对标量随机微分方程的欧拉预测器-校正器方案的双参数族的线性均方稳定性的完整分析研究。分析的族是根据控制方法隐性程度的两个参数给出的。对于参数的每次选择，都会获得稳定区域，并进行比较。通过减小步长而失去数值稳定性的反直觉事实的特定情况得到证实和证明。显示了 MS 稳定区域的图和证实理论结果的数值示例。