- Conceptualize the problem mathematically and physically and give a rigorous but perhaps implicit set of equations describing it.
- Select a numerical algorithm, that is, an explicit arithmetical procedure (which may be approximate) to replace these rigorous mathematical expressions.
- Do a numerical analysis to estimate the precision of the approximation process by means of an investigation of the role of errors introduced by the procedure (truncation errors) and by the machine (round-off errors).
- Determine the scale factors so that the mathematical expressions do not assume values that fall outside the fixed range of the computer at any time during the course of the computation.
- Do the dynamic analysis by drawing a flow diagram.
- Write the static code and enter it into the machine.
Description of programming from ‘Planning and Coding of Problems for an Electronic Computing Instrument’ by Goldstine and von Neumann, 1947-48. Quoted in ‘John von Neumann and the Origins of Modern Computing’ by William Aspray (MIT Press, 1990).