| 求解对流扩散方程的混合三次B-样条配点法 |
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| 引用本文： | 吴蓓蓓,徐 丽. 求解对流扩散方程的混合三次B-样条配点法[J]. 计算机工程与应用, 2018, 54(24): 41-45. DOI: 10.3778/j.issn.1002-8331.1712-0347 |
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| 作者姓名： | 吴蓓蓓 徐 丽 |
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| 作者单位： | 1.上海电力学院 数理学院，上海 200090 2.同济大学 数学科学学院，上海 200092 |
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| 摘 要： | 通过对三次B-样条和三次三角B-样条基函数引入权因子[ω]，给出了对流扩散方程的混合三次B-样条配点法。对对流扩散方程空间离散采用混合三次B-样条配点法和时间离散采用向前有限差分，引入参数[θ]，建立差分格式。对差分格式的稳定性进行分析，得到稳定性条件。数值实验表明所构造方法的有效性，并且适当调整权因子[ω]和参数[θ]的值，可提高计算的精度。
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| 关 键 词： | 对流扩散方程 三次B-样条 三次三角B-样条 有限差分 权因子 |
Hybrid cubic B-spline collocation method for solving convection-diffusion equation |
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| WU Beibei,XU Li. Hybrid cubic B-spline collocation method for solving convection-diffusion equation[J]. Computer Engineering and Applications, 2018, 54(24): 41-45. DOI: 10.3778/j.issn.1002-8331.1712-0347 |
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| Authors: | WU Beibei XU Li |
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| Affiliation: | 1.School of Mathematics and Physics, Shanghai University of Electric Power, Shanghai 200090, China2.School of Mathematical Science, Tongji University, Shanghai 200092, China |
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| Abstract: | A hybrid cubic B-spline collocation method is developed for the convection-diffusion equation by introducing the weight [ω] into the cubic B-spline and cubic trigonometric B-spline basis functions. The convection-diffusion equation is fully-discretized by using the hybrid cubic B-spline collocation for spatial discretization and the forward finite difference for the time discretization. A difference scheme is obtained by means of parameter [θ]. The stability of difference scheme is analyzed and the stability condition is given. The results of a numerical experiment are illustrated the validity of the constructed method. The accuracy of calculation can be improved by properly adjusting the values of the weight [ω] and the parameter [θ]. |
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| Keywords: | convection-diffusion equation cubic B-spline cubic trigonometric B-spline finite difference weight |
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