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A Numerical Solution of d2y/dx2=F(x)

Published online by Cambridge University Press:  03 November 2016

P. Stein
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Extract

In cases where successive integration of F(x) is not practical, a solution of the equation d2y/dx2=F(x) is obtained by approximation. The solution attempted is to find the value of y at selected points in the range of integration. A common procedure is to reduce the problem to the solution of a set of linear simultaneous equations, and these equations are then solved by “relaxation”. It does not appear to be generally known that an explicit and simple solution of these simultaneous equations exists. In this note the detail of such a solution is carried out for functions F(x) as occur in the theory of thin beams.

Type
Research Article
Information
The Mathematical Gazette , Volume 39 , Issue 329 , September 1955 , pp. 203 - 206
Copyright
Copyright © The Mathematical Association 1955

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References

† A six sided solid whose faces are parallelograms.