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

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.