The approximate solution of linear differential equations by the use of functionals

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1941
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Thorne, Charles
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Mathematics
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Abstract

The general functional method as it applies to solutions for differential equations is outlined;The equations arrived at by the use of the Ritz, Boussinesq, and Trefftz methods are obtained by the functional method;Other known applications of the functional method are listed;The functional method is used to obtain an approximate solution involving seventeen constants for the deflection of an infinite, corner loaded plate resting on an elastic foundation;The deflection is given for four values of Poisson's ratio and plotted for these values at x = 0, and x = y;Shearing stresses and moments along the lines x = 0, x = y are given and plotted for four values of Poisson's ratio;A discussion of the accuracy of the results is included. An error function is plotted for those original conditions of the problem which are not satisfied within the accuracy of the numerical calculations;An approximate solution of the system of differential equations with an undetermined convergence factor and containing the evaluation of sixteen constant coefficients is given for Poisson's ratio of .2, .25 and .3;An approximate solution of the system of differential equations involving thirty-one unknowns is obtained by means of the functional method and the corresponding set of linear equations is given but not solved. The solution for this set of equations would give a more accurate approximation to the problem.

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Wed Jan 01 00:00:00 UTC 1941