Numerical Solution of the Boundary Value Problem for the Potential Equation by Means of Punched Cards
- 1 August 1943
- journal article
- research article
- Published by AIP Publishing in Review of Scientific Instruments
- Vol. 14 (8) , 248-250
- https://doi.org/10.1063/1.1770174
Abstract
In this paper there is described in detail a method of obtaining numerical solutions of the boundary value problems for the potential equation ∂2u/∂x2+∂2u/∂y2=0 by means of punched cards. The differential equation is replaced by a finite difference equation and for a sufficiently fine net the value of the solution is assumed reasonably close to the known boundary values. These net point values are transferred onto punched cards and by repeated machine operations successive approximations are computed mechanically. When two successive approximations differ only in decimal places beyond the significant figure, the process is completed. A test example involving 145 net points required somewhat under 30 minutes of machine time per approximation. The method is suitable for use with standard I.B.M. or Remington Rand equipment.Keywords
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