The Genetic Algorithms For Solving Inverse Problem Of Parobolic Equation

There are many problems can be described by the partial 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. But in fact, if the operator the right term, the boundary condition or the initial condition is not known and the solution of the equation isn' t known either, the partial differential equation becomes an inverse problem. These inverse problems are ill-posed in the sense of Hadamard, and they represent primarily that the 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 aspects because the inverse problem is nonlinear and ill-posed, and how to solve these problem becomes a new field that mathematics learners, natural science researchers and engineering technology learners try to study.Now, there are many methods for solving inverse problem at home and abroad, such as select method, para-solution method, and Tikhonovregularization method, PST and disturb method are also numerical methods for solving this kind of problems. But each of these methods has its shortage. Genetic Algorithms can be used for solving mathematics problem, but the literatures about solving inverse problem by Genetic Algorithms are a few, so this article puts forward a new method for solving inverse problem. In this paper, the inverse problem of partial differential equation is described by the Genetic Algorithms, the inverse problem of parabolic function is solved by the usage of the Genetic Algorithms, and simulates four kinds of the inverse problem of parabolic function. 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 appl i cat ion. This will play an important role in the study of the inverse problem.