In 1939 Krylov became an honoured scientist of the Ukranian Soviet Socialist Republic.
He worked mainly on interpolation and numerical solutions to differential equations, where he obtained very effective formulas for the errors.
He also applied his methods to non-linear oscillatory problems in 1932 and, in so doing, laid the foundations for non-linear mechanics.
Krylov published over 200 papers on analysis and mathematical physics.
List of References (8 books/articles)
Article by: J.J. O'Connor and E.F. Robertson
Source: MacTutor History of Mathematics archive