# method of difference

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## method of difference

One of philosopher John Stuart Mills’ five methods of induction, intended to illustrate the concept of causation. The method of difference states: “if an instance in which the phenomenon under investigation occurs, and an instance in which it does not occur, have every circumstance in common save one, that one occurring in the former, the circumstance in which alone the two instances differ is the effect, or the cause, or an indispensable part of the cause, of the phenomenon.”
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In fact the essence of the method of differences for the solution of differential equations is that instead of solving a differential equation one solves a corresponding finite difference equation that is obtained by substituting differences expressions with higher or lower level of accuracy for the derivatives.
The method of differences is especially suitable for the solution of boundary value problems, for instance, the problem of determining a function that satisfies the Laplace equation in the interior of a given field [OMEGA] and possesses given values at the boundary of the field; such problems arise in the exploration of stationary temperature distribution when the temperature at the boundary of the field is known, in investigating the tension in a twisted rod of prismatic section, etc.
Each country studied in the papers differs from the others in some respects, providing the variation necessary to account for the differences in response, but all have an underlying unity due to their common European heritage, permitting something like an application of John Stuart Mill's "Method of Differences" or ceteris paribus experiment.
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