摘要翻译:
本文分析了四种常用的ADI格式在求解含混合导数项的含时多维扩散方程时的无条件稳定性。考虑混合导数系数的实际大小,得到了各格式参数θ的充要条件。我们的结果推广了Craig&Sneyd(1988)和Not Hout&Welfert(2009)的结果。数值实验证明了我们的主要定理。
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英文标题:
《Stability of ADI schemes for multidimensional diffusion equations with
mixed derivative terms》
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作者:
Karel in 't Hout, Chittaranjan Mishra
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最新提交年份:
2012
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分类信息:
一级分类:Mathematics 数学
二级分类:Numerical Analysis 数值分析
分类描述:Numerical algorithms for problems in analysis and algebra, scientific computation
分析和代数问题的数值算法,科学计算
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一级分类:Quantitative Finance 数量金融学
二级分类:Computational Finance 计算金融学
分类描述:Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法,包括蒙特卡罗,偏微分方程,格子和其他数值方法,并应用于金融建模
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英文摘要:
In this paper the unconditional stability of four well-known ADI schemes is analyzed in the application to time-dependent multidimensional diffusion equations with mixed derivative terms. Necessary and sufficient conditions on the parameter theta of each scheme are obtained that take into account the actual size of the mixed derivative coefficients. Our results generalize results obtained previously by Craig & Sneyd (1988) and In 't Hout & Welfert (2009). Numerical experiments are presented illustrating our main theorems.
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PDF链接:
https://arxiv.org/pdf/1205.1163