一类高阶椭圆型方程特征值的多项式特解法  

POLYNOMIAL PARTICULAR SOLUTIONS FOR SOLVING EIGENVALUE PROBLEM OF A CLASS OF HIGHER ORDER ELLIPTIC EQUATIONS

作　　者：张姊同 曹艳华 朱挺欣 ZHANG Zi-tong;CAO Yan-hua;ZHU Ting-xin(School of Sciences,East China Jiaotong University,Nanchang,Jiangxi 330013,China)

机构地区：[1]华东交通大学理学院,江西南昌330013

出　　处：《井冈山大学学报（自然科学版）》2022年第2期8-14,共7页Journal of Jinggangshan University (Natural Science)

基　　金：国家自然科学基金项目(11461026);江西省研究生创新资金项目(YC2020-S313)。

摘　　要：通过给出一种求解高阶椭圆型偏微分方程特征值的多项式特解法,使用多项式特解作为基函数对2阶、4阶、6阶和8阶椭圆型偏微分方程进行求解,同时采用多尺度技巧降低系数矩阵的条件数,得到了稳定的数值解。数值算例表明该算法在求解高阶偏微分方程特征值问题时具有精度高、效果好等方面的优越性,进一步证明了多项式特解法具有较高的精度和良好的稳定性。The paper presents a method of polynomial particular solutions(MPPS)for eigenvalue problem of higher order elliptic partial differential equations.The second,fourth,sixth and eighth order elliptic partial differential equations are solved by using the polynomial particular solutions as the basis function,while the condition number of the coefficient matrix is reduced by using the multiscale technique,and a stable numerical solution is obtained.Numerical examples show that the algorithm has the advantages of high accuracy and good effect in solving eigenvalue problems of high-order partial differential equations,it is further proved that the polynomial particular solutions have high accuracy and good stability.

关 键 词：高阶椭圆型偏微分方程 特征值:多项式特解法 

分 类 号：O241.82[理学—计算数学]