The Research Of Numerical Solutions For Inverse Parabolic Problem

There are many problems can be described by the partial differential equation in the natural science and engineering technology field, studying the numerical solution of these partial differential equations is a strong tool for solving these problems. How to get the numerical solution of these partial differential equations has been become a special subject and many researchers at home and abroad study in this field. All kinds of numerical methods and the recent research results are used to solve this kind of problems.But in fact, if the operator, the right term, the boundary condition or the initial condition is partially unknown and the solution of the equation is unknown either, the partial differential equation becomes an inverse problem. 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 problems is nonlinear and ill-posed, and how to solve these problems becomes a new field that natural science researchers and engineering technicians try to study.In this paper, we used the finite difference method to study the numerical solution of an inverse parabolic problem with Neumann boundary conditions. If one of boundary conditions is considered as unknown function, it is desirable to be able to determine more than one parameter from the given data. Therefore numerical results demonstrate that the process which is decrypted above to solve the complex inverse problems has high accuracy and good stability. This article studies the numerical solution to one-dimensional parabolic inverse problem by forward time centered space scheme. The stability and convergence of the difference scheme are proved with the maximum principle. The convergence order is O (τ+ h~2)in discrete norm L~∞. In addition, a numerical experiment demonstrates the theoretical results.