An investigation of the efficiency of digital computers and programs for the solution of partial differential equations by iterative methods

A large number of different computation procedures can usually be found to solve a given set of equations on a particular machine. For a given machine system the efficiency of a procedure can be measured by the time it takes to solve the problem employing that procedure. This time depends on the parameters defining the procedure and on such parameters defining the machine system as memory size, tape speed, etc. In this paper the interrelation between parameters defining a computation procedure and parameters defining a machine system is investigated for a class of problems in a systematic way. Efficient procedures are found for a given machine system and the relative efficiency of various systems is discussed.