基于五次B样条的对流-扩散方程数值解法  

Numerical solutions of the convection-diffusion equation based on quintic B-splines

作　　者：钱江[1] 王永杰 QIAN Jiang;WANG Yongjie(College of Science,Hohai University,Nanjing Jiangsu 211100,China)

机构地区：[1]河海大学理学院,江苏南京211100

出　　处：《阜阳师范大学学报（自然科学版）》2022年第1期1-10,共10页Journal of Fuyang Normal University:Natural Science

基　　金：江苏省自然科学基金青年基金项目(BK20160853);河海大学中央高校业务费基金项目(2016B08714,2019B19414);海岸灾害与防护教育部重点实验室开放基金(202011)。

摘　　要：基于五次B样条函数,提出一种求解对流-扩散方程的五次B样条方法。先利用光滑余因子协调法,给出有界闭区间上的具有均匀节点的五次B样条基函数表达式。接着计算在有界闭区间两端点处具有重节点的B样条基函数表达式。最后,将五次B样条基函数应用于求解一类对流扩散方程,在此过程中,按时间步长τ对对流-扩散方程进行离散,建立五次B样条逼近格式,由此提升数值方法的精度。Based on the quintic B-spline function,a quintic B-spline method for solving the convection-diffusion equation is proposed.Firstly,the smooth cofactor coordination method is used to give a quintic B-spline basis with uniform nodes on a bounded closed interval function expression.Secondly,the B-spline basis functions with multiple nodes at the two ends of the bounded closed interval are calculated.Finally,the quintic B-spline basis functions are considered to solve a class of convection diffusion equations.In this process,the convection-diffusion equation is discretized according to the time stepτ,and then the quintic B-spline approximation format is established.Hence,the precision of the numerical method is improved.

关 键 词：光滑余因子协调法 五次B样条 对流-扩散方程 微分方程数值解 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]