四阶抛物型方程基于子域精细积分方法的五次非多项式样条解

基于子域精细积分理论,利用五次非多项式样条函数关系式,给出了一个求解四阶抛物型方程周期初值的含参数α0的无条件稳定的差分格式.该格式为2层十点的隐格式.随后通过稳定性分析和误差分析,从理论上说明该格式是无条件稳定的,其局部截断误差为O(α(Δt)+(Δt)2+(Δx)6),其中Δt、Δx分别为时间步长和空间步长.结果表明,本文构造的格式是有效且实用的.

Non-polynomial quintic spline solution for four order parabolic equations based on the sub-domain precise integration method

Based on sub-domain precise integration theory and non-polynomial quintic spline,a unconditional stable scheme containing parameter α>0 for solving the periodic initial value problem of four order parabolic equation was presented.The different scheme was ten-point and two level implicit scheme.The result showed that this scheme was unconditionally stable,and the local truncation error was O(α(Δt)+(Δt)2+(Δx)6).Some examples showed that the scheme constructed in this paper was effective and practicable.