Mysteries of Academician Godunov

Academician Sergey Konstantinovich Godunov is an outstanding Russian scientist, a classic in the world of mathematical science, and a recognized leader in modern applied mathematics. He is known worldwide for his research in ordinary differential equations, partial differential equations, computational mathematics, continuum mechanics, and linear algebra. His contributions include methods for calculating critical parameters of nuclear devices, the general theory of difference schemes for solving differential equations, and the theory of elasticity. The difference scheme created by S.K. Godunov for calculating discontinuous solutions of gas dynamics equations using the "through-counting" method with adequate "smoothing" of shock waves gained worldwide fame as the Godunov scheme. These memoirs are dedicated to the last years of Sergey Konstantinovich's life, our joint work on the linearized Godunov scheme, and impressions from personal communication with Academician S.K. Godunov.