On the Measured

abstract The key to the method of measured equation of invariance (MEI) is the postulate: \the MEI is invariant to the excitation". In this paper, we proved that the MEI is independent of the excitation with the error bounded by O(h 2), where h is the discretization step. We also proved that the consistent condition jjLL?M=h 2 jj = ", where L is the partial diierential operator, and M the equivalent MEI operator. If the MEI coeecients C i (i = 1; : : : ; 4) are determined from the special distribution named metrons on the boundary of the object, then " = J(s), otherwise " = J(s), where J(s) is a functional of the source distribution s, and J(s) is the perturbation of the functional J(s). And nally we pointed out that the error between the accurate solution and the solution of MEI is bounded by two terms, one is caused by the FD approximation at interior nodes which is proportional to h 2 , another is caused by MEI and is independent of h but proportional to J(s) which ensured the accuracy of MEI solution.