| 三维抛物型方程的一个高精度恒稳定的PC格式 |
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| 引用本文： | 马明书,孟燕玲,朱霖霖.三维抛物型方程的一个高精度恒稳定的PC格式[J].纯粹数学与应用数学,2009,25(3):459-463. |
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| 作者姓名： | 马明书 孟燕玲 朱霖霖 |
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| 作者单位： | 河南师范大学数学与信息科学学院,河南,新乡,453007 |
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| 基金项目： | 河南省教育厅自然科学基础研究基金 |
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| 摘 要： | 对三维抛物型方程，构造了一个高精度恒稳定的PC格式，格式的截断误差阶达到O（△t^2＋△x^4），通过数值实例验证了所得格式较现有的同类格式的精度提高了二位以上有效数字；然后将Richardson外推法应用于本文格式，得到了具有O（△t^3＋△x^6）阶精度的近似解，并将所得格式推广到了四维情形．
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| 关 键 词： | 抛物型方程 PC格式 截断误差 恒稳定 |
A PC scheme of high accuracy with absolutely stable for solving parabolic equation of three-dimension |
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| MA Ming-shu,MENG Yan-ling,ZHU Lin-lin.A PC scheme of high accuracy with absolutely stable for solving parabolic equation of three-dimension[J].Pure and Applied Mathematics,2009,25(3):459-463. |
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| Authors: | MA Ming-shu MENG Yan-ling ZHU Lin-lin |
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| Institution: | MA Ming-shu,MENG Yan-ling,ZHU Lin-lin(College of Mathematics , Information Science,Henan Normal University,Xinxiang 453007,China) |
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| Abstract: | This paper presents a PC scheme of high accuracy for solving parabolic equation of three-dimension. The scheme is absolutely stable and the truncation error for the method is O（△t^2 ＋ △x^4）; Then Richardson＇s extrapolation method is successfully applied to the scheme and the approximate solution with accuracy O（△t^3 ＋ △x^6） is gained with once extrapolation. Finally, the scheme is generalized to solve parabolic equation of fourdimention. |
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| Keywords: | parabolic equation PC scheme truncation error absolutely stable |
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