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首页> 外文期刊>Review of Scientific Instruments >Numerical Solution of the Boundary Value Problem for the Potential Equation by Means of Punched Cards
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Numerical Solution of the Boundary Value Problem for the Potential Equation by Means of Punched Cards

机译：冲卡解势方程边值问题的数值解

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摘要

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.
机译：在本文中，详细描述了一种通过打孔卡获得势方程∂2u/∂x2+∂2u/∂y2= 0的边值问题的数值解的方法。微分方程被有限差分方程代替，对于足够精细的网络，假定解的值合理地接近已知边界值。这些净点值被转移到打孔卡上，通过重复的机器操作，机械地计算出连续的近似值。当两个连续的近似值仅在超出有效数字的小数位不同时，该过程完成。一个包含145个净点的测试示例，每次近似值需要30分钟的机器时间。该方法适用于标准I.B.M.或Remington Rand设备。

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