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  

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

作　　者：林丽烽[1] 

机构地区：[1]福建农林大学计算机与信息学院,福建福州350002

出　　处：《福建农林大学学报（自然科学版）》2010年第4期444-448,共5页Journal of Fujian Agriculture and Forestry University:Natural Science Edition

摘　　要：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α>0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.Based on sub-domain precise integration theory and non-polynomial quintic spline,a unconditional stable scheme containing parameter α0 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.

关 键 词：四阶抛物型方程 子域精细积分 五次非多项式样条 稳定性分析 误差分析 

分 类 号：O241.8[理学—计算数学]