| 对流扩散方程的三次样条差分格式 |
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| 引用本文： | 齐远节,刘利斌,曹怀火.对流扩散方程的三次样条差分格式[J].阜阳师范学院学报(自然科学版),2011,28(1):47-49. |
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| 作者姓名： | 齐远节 刘利斌 曹怀火 |
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| 作者单位： | 齐远节,QI Yuan-jie(池州市第一中学);刘利斌,曹怀火,LIU Li-bin,CAO Huai-huo(池州学院,数学计算机科学系,安徽,池州,247000) |
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| 摘 要： | 提出了两种新的求解对流扩散方程的三次样条差分格式.首先利用变换将对流扩散方程变为扩散方程,然后分别结合二阶和四阶精度的三次样条公式获得两个无条件稳定的差分格式,其局部截断误差分别为0(t2+h2)和0(t2+h4).数值实验表明,文中方法优于以往的三次样条方法.
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| 关 键 词： | 对流扩散方程 三次样条 差分格式 稳定 |
Cubic spline difference scheme of convection-diffusion equation |
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| QI Yuan-jie,LIU Li-bin,CAO Huai-huo.Cubic spline difference scheme of convection-diffusion equation[J].Journal of Fuyang Teachers College:Natural Science,2011,28(1):47-49. |
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| Authors: | QI Yuan-jie LIU Li-bin CAO Huai-huo |
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| Institution: | QI Yuan-jie1,LIU Li-bin2,CAO Huai-huo2(1.The First Middle School of Chizhou City,Chizhou Anhui 247000,China,2.Department of Mathematics and Computer Science,Chizhou College,China) |
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| Abstract: | Two new methods are presented for solving convection-diffusion equation.Firstly,a functional transformation is introduced and the convection-diffusion equation is transferred to the diffusion equation.Then,by utilizing the cubic spline difference formula of two and four order accuracy,two unconditionally stable schemes are obtained.The local truncation error of the new methods are O(t2+h2)and O(t2+h4).Numerical experiment shows that the new methods are better than some other cubic spline methods. |
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| Keywords: | convection-diffusion cubic spline difference scheme stability |
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