求解对流扩散方程的混合三次B-样条配点法  

Hybrid cubic B-spline collocation method for solving convection-diffusion equation

作　　者：吴蓓蓓[1,2] 徐丽[1] WU Beibei;XU Li(School of Mathematics and Physics,Shanghai University of Electric Power,Shanghai 200090,China;School of Mathematical Science,Tongji University,Shanghai 200092,China)

机构地区：[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

出　　处：《计算机工程与应用》2018年第24期41-45,共5页Computer Engineering and Applications

基　　金：国家自然科学基金(No.11502141)

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。A hybrid cubic B-spline collocation method is developed for the convection-diffusion equation by introducing the weight co 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-splme 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.

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 

分 类 号：O241.82[理学—计算数学]