The Numerical Computation Methods For A Kind Of Parabolic Inverse Problem

With the deep development of mathematics in practical application, inverse problem ofmathematics physics becomes a more and more important subject. In resent years, the application ofinverse problem has permeated into the fields such as industrial design, earth physics, material science,biomedical and so on. But because of its complexity, its application has been limited in many aspects,however, more and more scholars have been attracted to research this problem. From1960s to now, thepeople who study inverse problems are more and more, the ways of solving inverse problems are also moreand more, inverse problem develops into a dependent subject.In the introduction of first chapter, we briefly introduce the meanings and ways of studyinginverse problems, and then list the classification of inverse problem in different points. Finally we show itsapplication with two examples.In chapter two, the restrained optimal perturbation method is proposed to study the backward heatconduction inverse problem. We also give the numerical experiment in the end of chapter two. Becauseparameter inverse problems have been wildly used in practical application. In chapter three of this paper,we introduce the restrained optimal parameter perturbation method, which based on the restrained optimalperturbation method, and introduce an optimization algorithm——Difference Evolution which will be usedin the process of computation; In chapter four, we apply the restrained optimal parameter perturbationmethod to solve a kind of parabolic parameter inverse problem with resource term, and check the feasibilityand stability of this method by numerical experiment.In the end, give the summary of this paper, and look forward to the work in the future.