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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In numerical analysis and computational fluid dynamics, Godunov''s theorem also known as Godunov''s order barrier theorem is a mathematical theorem important in the development of the theory of high resolution schemes for the numerical solution of partial differential equations.Professor Sergei K. Godunov originally proved the theorem as a Ph.D. student at Moscow State University. It is his most influential work in the area of applied and numerical mathematics and has had a major impact on science and engineering, particularly in the development of methodologies used in computational fluid dynamics (CFD) and other computational fields. One of his major contributions was to prove the theorem (Godunov, 1954; Godunov, 1959), that bears his name.