Reminiscences about numerical schemes

TL;DR

This paper recounts the historical development and personal recollections of the early numerical schemes, particularly Godunov's scheme, from the 1950s to 1969, highlighting modifications and scientific collaborations.

Contribution

It provides a detailed historical account and personal insights into the development and modifications of Godunov's numerical scheme from 1953 to 1969.

Findings

Historical development of Godunov's scheme described

Personal contributions and modifications detailed

Collaborative efforts at the Institute of Applied Mathematics highlighted

Abstract

This preprint appeared firstly in Russian in 1997. Some truncated versions of this preprint were published in English and French, here a fully translated version is presented. The translation in English was done by O. V. Feodoritova and V. Deledicque to whom I express my gratitude. In the present paper I will describe how the first variant of the Godunov's scheme has been elaborated in 1953-1954 and tell about all modifications realized by myself (until 1969) and the group of scientists from the Institute of Applied Mathematics in Moscow (which has become the M.V.Keldysh Institute of Applied Mathematics).