About: Godunov's theorem

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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. The theorem states that: Linear numerical schemes for solving partial differential equations (PDE's), having the property of not generating new extrema, can be at most first-order accurate.

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  • 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. The theorem states that: Linear numerical schemes for solving partial differential equations (PDE's), having the property of not generating new extrema, can be at most first-order accurate. 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 methods 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. (en)
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  • 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. The theorem states that: Linear numerical schemes for solving partial differential equations (PDE's), having the property of not generating new extrema, can be at most first-order accurate. (en)
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  • Godunov's theorem (en)
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