An algorithm for recovering the characteristics of the initial state of supernova

An optimization method for the numerical solution of the inverse problem of recovering the initial state of a supernova is proposed. The gradient of the inverse problem objective functional is constructed. The solution of the direct and adjoint problems is based on a combination of the large particle method, Godunov's method, and piecewise parabolic method on a local stencil. Results of the verification of the proposed numerical method and the results of numerical solution of the Evrard and Sedov collapse problems are presented.