O(h～6) And O(h～8) Correction Method For Eigenvalue Problems Of Elliptic Equations

In this paper, some correction methods for elliptic problems areintroduced. Then, a sixth order correction method for eigenvalue problems of Helmholtz equations with variable coefficients is constructed. The correction procedure only needs to compute little work, but the precision is much higher than uncorrection. However a posteriori error can be obtained by this method. In the end, a eighth order correction method for eigenvalue problems of Helmholtz equations with constant coefficients is introduced.