**Input-Output Buffering and Fortran**

David E. Ferguson

Pages: 1-9

DOI: 10.1145/321008.321009

**Changing from Analog to Digital Programming by Digital Techniques**

Marvin L. Stein, Jack Rose

Pages: 10-23

DOI: 10.1145/321008.321010

**Sequential Machines, Ambiguity, and Dynamic Programming**

Richard Bellman

Pages: 24-28

DOI: 10.1145/321008.321011

Given a sequential machine, in the terminology of E. F. Moore, Annals of Mathematics Studies, No. 34, 1956, a problem of some interest is that of determining testing procedures which will enable one to transform it into a known...

**On the Increase of Convergence Rates of Relaxation Procedures for Elliptic Partial Difference Equations**

M. L. Juncosa, T. W. Mullikin

Pages: 29-36

DOI: 10.1145/321008.321012

Occasionally in the numerical solution of elliptic partial differential equations the rate of convergence of relaxation methods to the solution is adversely affected by the relative proximity of certain points in the grid. It has been proposed...

**Boundary Contraction Solution of Laplace's Differential Equation II**

Tse-Sun Chow, Harold Willis Milnes

Pages: 37-45

DOI: 10.1145/321008.321013

In this paper the numerical solution of Laplace's equation for the circle is discussed and consideration is given to the convergence of the solution obtained by the boundary contraction method to the analytic solution. It is proved that in order...

**Stability of a Numerical Solution of Differential Equations—Part II**

W. E. Milne, R. R. Reynolds

Pages: 46-56

DOI: 10.1145/321008.321014

In Part I of this paper [1] the authors have shown that instability in Milne's method of solving differential equations numerically [2] can be avoided by the occasional use of Newton's “three eights” quadrature formula. Part I dealt...

**A Generalization of a Theorem of Carr on Error Bounds for Rung-Kutta Procedures**

B. A. Galler, D. P. Rozenberg

Pages: 57-60

DOI: 10.1145/321008.321015

In [1] Carr established propagation error bounds for a particular Runge-Kutta (RK) procedure, and suggested that similar bounds could be established for other RK procedures obtained by choosing the parameters differently. More explicitly, a...

**A Numerical Method for Solving Control Differential Equations on Digital Computers**

W. H. Anderson, R. B. Ball, J. R. Voss

Pages: 61-68

DOI: 10.1145/321008.321016

Frequently, as in missile control systems, linear differential equations are simultaneous with nonlinear but slower acting differential equations. The numerical solution of this type of system on a digital computer is significantly speeded up by...

**Truncation Error in the Graeffe Root-Squaring Method**

Gerard P. Weeg

Pages: 69-71

DOI: 10.1145/321008.321017

**Serial Correlation in the Generation of Pseudo-Random Numbers**

R. R. Coveyou

Pages: 72-74

DOI: 10.1145/321008.321018

Many practiced and proposed methods for the generation of pseudo-random numbers for use in Monte Carlo calculation can be expressed in the following way: One chooses an integer P, the base; an integer &lgr;, the multiplier,...

**A New Pseudo-Random Number Generator**

A. Rotenberg

Pages: 75-77

DOI: 10.1145/321008.321019

Although the multiplicative congruential method for generating pseudo-random numbers is widely used and has passed a number of tests of randomness [1, 2], attempts have been made to find an additive congruential method since it could be expected...

**Footnote to a Recent Paper**

H. H. Goldstine

Pages: 78-79

DOI: 10.1145/321008.321020

In a recent paper1 I stated that von Neumann had originated the suggestion for the use of Schur's canonical form for arbitrary matrices. I have since learned that the suggestion actually is due in the first instance to John...