A letter sent March 11, 1947, from John von Neumann to Richtmyer outlined a technique for approximating complex problems being studied at Los Alamos by Stanislaw Ulam. Richtmyer used the massive IBM SSEC calculator for some of the first large-scale uses of what would be called the Monte Carlo method.[5]
He was the author of textbooks including Principles of Advanced Mathematical Physics in 1978.
In 1990 he was awarded the Leroy P. Steele Prize from the American Mathematical Society for his book Difference Methods for Initial-Value Problems.[9]
J. VonNeumann, R. D. Richtmyer (1950). A Method for the Numerical Calculation of Hydrodynamic Shocks. Journal of Applied Physics, Vol. 21, No. 3., pp. 232–237.(Classic article on the numerical solution of hydrodynamic problems)
R. D. Richtmyer (1960). "Taylor instability in a shock acceleration of compressible fluids", Communications on Pure and Applied Mathematics 13, 297–319. (Predicted the Richtmyer–Meshkov instability)
R. D. Richtmyer and K. W. Morton (1967). Difference Methods for Initial-Value Problems. Second edition. Wiley-Interscience.
R. D. Richtmyer (1967). Stability of a New Radio Flash Code. Los Alamos Scientific Laboratory, NM (LA-3864-MS).
R. D. Richtmyer (1978), Principles of Advanced Mathematical Physics Vol. 1 & 2, Springer-Verlag, New York.
^Richtmyer, Robert Davis (1935). Quantum Mechanical Study of Multiple-Ionization Collisions of a Fast Electron with an Atom. Massachusetts Institute of Technology. Bibcode:1935PhDT.........1R.