求解一维抛物型方程的高精度有限差分方法  

A high order finite difference method for solving the one-dimensional parabolic equation

作　　者：祁应楠[1] 

机构地区：[1]宁夏师范学院数学与计算机科学学院,宁夏固原756000

出　　处：《西北师范大学学报（自然科学版）》2016年第6期29-34,共6页Journal of Northwest Normal University(Natural Science)

基　　金：宁夏高等学校科学研究资助项目(NGY2015115);宁夏自然科学基金资助项目(NZ15259;NZ16251);宁夏师范学院科研项目(NXSFZD1603)

摘　　要：针对一维抛物型方程,采用样条函数近似和Padé公式,构造了一种高精度有限差分格式.该格式关于时间和空间均具有六阶精度,并且从理论上被证明是无条件稳定的.通过数值实验验证了本文方法的精确性和稳定性,与文献计算结果比较显示,本文格式的计算结果更加精确.A high order finite difference scheme for solving the one-dimensional parabolic equation is developed based on the Sextic spline functions for the spatial derivative and （3,3）Padeapproximation for the temporal derivative.The scheme is sixth order accuracy in both time and space,and the performance of unconditional stability is proved in theory.The accuracy and effectiveness of the present method are validated by three numerical experiments,the results show that the present method is more accurate than the methods in the literature.

关 键 词：抛物型方程 样条函数 PADE逼近 高精度 有限差分法 

分 类 号：O241.82[理学—计算数学]