1941 Numerical solvers for partial differential equations (PDE):  Hrennikoff, Alexander (1941). Solution of problems of elasticity by the framework method. Journal of Applied Mechanics. 8 (4): 169–175. Courant, R. (1943). Variational methods for the solution of problems of equilibrium and vibrations. Bulletin of the American Mathematical Society. 49: 1–23. doi:10.1090/s0002-9904-1943-07818-4.
1947 Numerical linear algebra: John von Neumann and Herman Goldstine, Numerical Inverting of Matrices of High Order (Bulletin of the AMS, Nov. 1947).
1953 Monte Carlo method: Metropolis, N.; Rosenbluth, A.W.; Rosenbluth, M.N.; Teller, A.H.; Teller, E. (1953). Equation of State Calculations by Fast Computing Machines. J. Chem. Phys. 21 (6): 1087-1092. doi: 10.1063/1.1699114.
1960-1970 The finite element method: FEM 60s and 70s:  Strang, Gilbert; Fix, George (1973). An Analysis of The Finite Element Method. Prentice Hall. ISBN 978-0-13-032946-2.
1970 Electronic structure methods in computational chemistry: Gaussian is a general-purpose computational chemistry software package initially released in 1970 by John Pople.  Publisher’s note: Sir John A. Pople, 1925-2004. Journal of Computational Chemistry. 25 (9): 2004. doi: 10.1002/jcc.20049.
1974-1977 The first molecular dynamics simulation of a realistic system; the first protein simulations. Stillinger, F. H. and Rahman, A. J. Chem. Phys. 60, 1545 (1974); McCammon, J. A., Gelin, B. R., and Karplus, M. Nature 267, 585 (1977)
1970s Development of linear algebra libraries: linear algebra package (LAPACK) https://en.wikipedia.org/wiki/LAPACK and basic linear algebra subprograms (BLAS). Lawson, C. L.; Hanson, R. J.; Kincaid, D.; Krogh, F. T. (1979). Basic Linear Algebra Subprograms for FORTRAN usage. ACM Trans. Math. Softw. 5 (3): 308–323. doi: 10.1145/355841.355847.
1980-2010 Development of parallel algorithms for linear algebra, Fourier transforms, N-body problems, graph theory [https://cvw.cac.cornell.edu/APC/]
2010-2020 Parallel algorithms for machine learning [https://cvw.cac.cornell.edu/APC/]