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

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.