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

Thumbnail Image
Thorne, Charles
Major Professor
Committee Member
Journal Title
Journal ISSN
Volume Title
Research Projects
Organizational Units
Organizational Unit
Welcome to the exciting world of mathematics at Iowa State University. From cracking codes to modeling the spread of diseases, our program offers something for everyone. With a wide range of courses and research opportunities, you will have the chance to delve deep into the world of mathematics and discover your own unique talents and interests. Whether you dream of working for a top tech company, teaching at a prestigious university, or pursuing cutting-edge research, join us and discover the limitless potential of mathematics at Iowa State University!
Journal Issue
Is Version Of

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.

Subject Categories
Wed Jan 01 00:00:00 UTC 1941