I am preparing a lecture course on the applications of operator theory where I intended to make some numerical analysis application. I was wondering about this question while browsing the literature I can access.
Lax and Richtmyer (1955) start with a vague reference to Courant, Friedrichs, and Lewy (1928).
Trotter (1958) on the other hand refers to von Neumann, without any specific reference.
Since I have no deeper background in numerical analysis, I might be missing some obvious point. So can someone tell me (with a reference) who introduced the notion of stability in numerical analysis?
Best Answer
John von Neumann is credited as having pioneered the stability analysis of finite difference schemes. Crank and Nicholson [1] acknowledge Von Neumann when they demonstrate the stability of their scheme in 1947, and a few years later the method was applied in a meteorological context in a paper co-authored by Von Neumann [2]. That 1950 paper introduces the stability analysis as being "patterned after the rigorous method of Courant, Friedrichs, and Lewy."
[1] J. Crank and P. Nicolson, Proc. Camb. Phil. Soc. 43, 50–67 (1947).
[2] J.G. Charney, R. Fjörtoft, and J. von Neumann, Tellus 2, 237-254 (1950). Online at http://mathsci.ucd.ie/~plynch/eniac/CFvN-1950.pdf
Further reading:
http://en.wikipedia.org/wiki/Von_Neumann_stability_analysis