01/01/1997 09:00 AM
Computer Science
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 || L phi - M phi /h^2 || = e, where L is the partial differential operator, and M the equivalent MEI operator. If the MEI coefficients C^*_i (i=1,...,4) are determined from the special distribution named metrons on the boundary of the object, then e = d J(s), otherwise e = J(s), where J(s) is a functional of the source distribution s, and d J(s) is the perturbation of the functional J (s). And finally we pointed out that the error between the accurate solution and the solution of ME I 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 d J(s) which ensured the accuracy of MEI solution.
