Landweber iteration method for solving operator equations L(U ̅ )=F

Аннотация

The article is devoted to one of the modern ways of research in the theory of ill-posed problems – inverse problems for hyperbolic equations. The solution of inverse problems was suggested by Landweber. The aim of this work is development of mathematical models and their efficient numerical methods for solving inverse problems of fundamental research. The research problem is to develop a mathematical model for solving inverse problems of Landweber method hyperbolic type; development of a numerical algorithm for solving nonlinear operator equations based on ENO; software implementation of numerical methods for solving these equations; explore and analyze the graphs produced during the study. The urgency of solving inverse problems for hyperbolic type equations by Landweber is caused by their decision – without the use of computer technology it is almost impossible and the only means for the study of complex unsteady nonlinear hyperbolic equations.