The Genetic Algorithms For Solving Inverse Problem Of Parabolic Equation

There are many problems can be described by the differential equation in the natural science and engineering technology field. Studying the numeric solution of these partial differential equations is a strong tool for solving these problems. Inverse problem of partial differential equation is an interdisciplinary and frontier science. It has great significance not only in theory but also in practice. How to solve the inverse problem of partial differential equation has been become a special course and many foreigners and researches studying in this field. All kinds of numerical methods and the last studying solutions are used to solve the inverse problem. These inverse problems are the ill-posed in the sense of Hadamard. and they represent primarily that solution does not depend continuously on the data i.e. the error between the solved approximation and the true value is very big when there is a small change in the right term, that is unstable. The theory and the solving solution of the inverse problem are more difficult than those of the direct problem and be related with many methods for solving inverse problem is nonlinear and ill-posed. Now, there are many methods for solving inverse problem at home and abroad, such as select method, para-solution method, and Tikhonov regularization method, PST and disturb method are also numerical methods for solving this kind of problems. But each of these methods has its shortage. So this article puts forward a new method for solving inverse problem.The genetic algorithm is a kind of searching method which simulates the natural evolution. It is simple and easy to implement, especially it do not need the special field knowledge, so it has been using in very broad fields. Now the genetic algorithm has got a lot of fruits and more scholars begin to pay attention to it. The genetic algorithm is still a new technology being in the development. Despite its success in so many domains, its theoretical groundwork is weak. There are still lots of problems to study and develop. This paper has done some work in the researching of theory and application of the genetic algorithm. Based on the study of the basic structure of the genetic algorithm, some improvement is given: two new concept, adaptive population and competing population. All above done, the paper gives a new framework of the genetic algorithm-propagate gene. In this paper the inverse problem of parabolic function is solved by the usage of the genetic algorithms. The test result indicates that the error between the true solution and the approximation obtained from the genetic algorithms is very small, and can reach a perfect extent. As a result, it is feasible in the practice application. This will play an important role in the study of the inverse problem.