| 抛物型方程的一个实用有效的高阶差分算法 |
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| 引用本文： | 汪子莲,丁双平.抛物型方程的一个实用有效的高阶差分算法[J].兰州工业高等专科学校学报,2008,15(1):1-5. |
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| 作者姓名： | 汪子莲 丁双平 |
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| 作者单位： | 1. 兰州工业高等专科学校,基础部,甘肃,兰州,730050
2. 甘肃省礼县教育局,甘肃,礼县,742200 |
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| 摘 要： | 针对文献1]的高阶差分算法，首先综合应用降维降阶法导出了抛物方程的一个不需要用到u在边界上的二阶导数的值、计算量小、精度高的有限差分格式，并给出了该差分格式的截断误差的表达式；然后通过引进过渡层给出了近似因式分解的交替方向隐差分格式的算法；最后是数值例子，数值结果和理论结果是吻合的．
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| 关 键 词： | 抛物型方程 高阶差分算法 差分格式 |
| 文章编号： | 1009-2269(2008)01-0001-05 |
| 修稿时间： | 2007年11月20 |
A Practical and Effective Algorithm of Higher-order Difference of Parabolic Equation |
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| WANG Zi-lian,DING Shuang-ping.A Practical and Effective Algorithm of Higher-order Difference of Parabolic Equation[J].Journal of Lanzhou Higher Polytechnical College,2008,15(1):1-5. |
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| Authors: | WANG Zi-lian DING Shuang-ping |
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| Affiliation: | WANG Zi - lian, DING Shuang - ping ( 1. The Basic Courses Department of Lanzhou Polytechnic College, Lanzhou 730050, China; 2. Lixian Education Bureau of Gansu Province, Lixian 742200, China) |
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| Abstract: | In view of the higher - order difference algorithm of article 1 ], firstly, this article comprehensively applies the method of reduction of order and reduction of dimension to develop limited difference scheme which shows a high accuracy and lower computing cost, not using the second derivative value on its boundary. Additionally, the difference scheme expressions of truncation error is presented;secondly, the algorithm of ADI （altemate direct implicit）difference scheme of approximate polynomials factorization is presented by introducing a variable of intermediate value; finally, a numerical example demonstrates the numerical results and theoretical results are inosculate. |
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| Keywords: | parabolic equation algorithm of higher - order difference difference scheme |
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