小波Galerkin方法在Sturm-Liouville边值问题紧积分算子中的应用  

Wavelet Galerkin algorithm and its application in compact integral operator with symmetrical kernel caused by the Sturm-Liouville boundary value problem

作　　者：夏茂辉[1] 孙凤燕[1] 

机构地区：[1]燕山大学理学院,秦皇岛066000

出　　处：《黑龙江大学自然科学学报》2013年第4期425-430,共6页Journal of Natural Science of Heilongjiang University

基　　金：秦皇岛市科技攻关计划资助项目(201001A035)

摘　　要：考虑一类由Sturm-Liouville边值问题引出的核对称紧积分算子。给出该类边值问题解的紧积分算子表达形式,构造小波Galerkin方法求解该类积分算子的特征值问题,利用周期构造法构造平方可积空间中的紧支集小波基,讨论特征值在该算法下的收敛性。通过实例验证了小波Galerkin方法在Sturm-Liouville边值问题紧积分算子中应用的可行性。Consider a compact integral operator with symmetrical kernel caused by the Sturm-Liouville boundary value problem, and give the compact integral operator expression about the solutions of the boundary value problem. The wavelet Galerkin method for solving the eigenvalue problem of this compact integral operator is developed, throughing the cycle constuction method to construct the compact support wavelet on the square integrable space, and discuss the convergence of the eigenvalue given by the method, finally by two examples to verify the feasibility of the wavelet Galerkin method applied in compact integral operator caused by the Sturm-Liouville boundary value problem.

关 键 词：STURM-LIOUVILLE边值问题 紧积分算子 特征值 小波Galerkin方法 

分 类 号：O241.83[理学—计算数学]