Research On Parameter Inversion Model For Two_Dimensional Parabolic Equation Using The Iterative Algorithm

In recent years, more and more attention has been put in a variety of inverse problems of differential equations, due to the need for practical engineering. Great progress has been made in research on the inverse problems. However, the inverse problem is nonlinear and ill-posed, and its development time is short. So many theories are not into the system. Moreover, some results also appear fragmentary. Therefore, to solve the inverse problem of differential equations is still a daunting task.In practical applications, the problem under investigation is often governed by partial differential equations. Hence the solution of practical inverse problems often leads inverse problems associated with partial differential equations. Two essential difficulties appear frequently. One is that the observation data possibly does not belong to the corresponding set to the exact solution, another is that the approximation is not stable. Namely, the little error of initial data due to our measure will lead to the deviation between approximate solutions and true solutions. Thus inverse problems are often ill-posed which makes inverse problem more difficult. Also just because of it, many scholars are committed to the study of inverse problem at home and abroad.In this paper, the iterative method was applied to solve the inverse problem of two-dimensional parabolic equation; the numerical solutions of solving the inverse problem have been got. Three methods are introduced for solving the inverse problem of the two-dimensional parabolic equation with variable coefficients in three chapters. In the third chapter, the best-disturbed iteration numerical method is used for solving the inverse problem, and gave the numerical solution. The method is successfully put into practice to solving the inverse problem of two-dimensional parabolic equation whose coefficient is partition paragraph function, it turns out that the best perturbation method is one of the efficient methods to solve this kind of problems; In chapterâ…£, Quasi-Newton method is introduced to the parameter inversion of two-dimensional parabolic equation parameter inversion, the number of iterations is less. Moreover, for the case with random noisy data, the inversion results are stable; In chapter V, Levenberg-Marquardt method is an effective algorithm for solving the inverse problem of the two-dimensional parabolic equation with variable coefficients, the number of iterations is small. This method have less dependence on the initial data, for the case with random noisy data, the inversion results are also stable.