| 带Neumann边界条件的抛物型方程的样条差分方法 |
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| 引用本文： | 刘蕤,高锐敏.带Neumann边界条件的抛物型方程的样条差分方法[J].郑州大学学报(自然科学版),2013(3):37-40,76. |
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| 作者姓名： | 刘蕤 高锐敏 |
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| 作者单位： | [1]郑州幼儿师范高等专科学校理科教学部,河南郑州450000 [2]北京师范大学教育管理学院,北京100875 [3]河南牧业经济学院基础部,河南郑州450044 |
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| 基金项目： | 河南省基础与前沿技术研究计划项目,编号132300410381 |
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| 摘 要： | 基于四次样条函数和广义梯形公式,针对抛物型方程的Neumann边值问题,构造了一族含参数θ（θ∈0,1]）的隐式差分格式,该格式在时间方向的精度为二阶,在空间方向的精度为四阶,当θ=1/3时,该差分格式在时间方向的精度可提高到三阶.数值实验表明方法是非常有效的.
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| 关 键 词： | 抛物型方程 四次样条函数 差分格式 Neumann边值问题 |
Spline Difference Method for Solving Parabolic Equations with Neumann Boundary Conditions |
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| LIU Rui,＇,GAO Rui-min.Spline Difference Method for Solving Parabolic Equations with Neumann Boundary Conditions[J].Journal of Zhengzhou University (Natural Science),2013(3):37-40,76. |
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| Authors: | LIU Rui ＇ GAO Rui-min |
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| Institution: | 3 ( 1. Department of Science Teaching, Zhengzhou Kindergarten Teacher＇ College, Zhengzhou 450000, China ; 2. College of Education Administration, Beifing Normal University, Beifing 100875, China ; 3. Department of Basic Course, Henan University of Animal Husbandry and Economy, Zhengzhou 450044, China) |
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| Abstract: | Based on the quartic spline function and generalized trapezoidal formulas, a family of implicit difference schemes, including parameter 0, 0 E 0, 1 ], for solving parabolic equation with Neumann boundary conditions were constructed. The accuracy of these schemes was second-order in time direction and fourth-order in space direction. If 0 = 1/3, the accuracy of this scheme in time direction was im- proved to third-order. At last, the numerical results showed that our methods were very efficient. |
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| Keywords: | parabolic equation quartic spline function difference scheme Neumann boundary condition |
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