An iterative numerical algorithm for solving multi-parameter inverse problems of evolutional partial differential equations

Abstract

The iterative numerical algorithm of the pulse-spectrum technique (PST) is extended and developed to solve the multi-parameter inverse problems of one-dimensional evolutional partial differential equations (wave equations or diffusion equations). It has the practical advantages of universality, economy of programing, economy of data acquisition, and economy of computing costs. Without the real measurement data, numerical simulations are carried out only for the two-parameter inverse problems of a one-dimensional linear wave equation to test the feasibility and to study the general characteristics of the PST. It is found that the PST does give excellent results and it is as robust as in the single parameter case.