Reconstructing The Initial State For The Nonlinear System And Analyzing Its Convergence

An algorithm to reconstructing the initial state of the nonlinear system isdescribed, and the iteration algorithm is based on the the basic concept of theobservers using the known output value on the specific domain. Firstly the for-ward and backward observers system are constructed and their nudging termscan be proved close to zero. Then the observers are used alternately and repeat-edly to solve the approximation problem in n times until the error estimate isinfinitesimal. The convergence is also analyzed under the right conditions andthe example model is solved by numerical methods through MATLAB program.At last, for the more accurate convergence analysis, the spatial variable x andthe time variable t are considered separately through FEM, and are used in thesemi-discretization and full-discretization in space accordingly. Also, the methodof parametric selection was analyzed.