Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-28T04:59:59.833Z Has data issue: false hasContentIssue false
  • English
  • Français

A Note on the Numerical Solution of Fourth Order Differential Equations

Published online by Cambridge University Press:  07 June 2016

L. C. Woods
L. C. Woods*
Affiliation:
Department of Applied Mathematics, University of Sydney
Get access

Summary

An old numerical method of solving fourth order differential equations is put in relaxation form. The higher order correction terms are included and the technique is illustrated by an example. The method has the advantage of being more rapidly convergent than the usual relaxation procedure for fourth order equations. Some comments are made on the numerical solution of the viscous flow equation.

Type
Research Article
Information
Aeronautical Quarterly , Volume 5 , Issue 4 , September 1954 , pp. 176 - 184
Copyright
Copyright © Royal Aeronautical Society. 1954

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Fox, L. (1950). The Numerical Solution of Elliptic Differential Equations when the Boundary Conditions Involve a Derivative. Phil. Trans., 242A, pp. 345–378, 1950.Google Scholar
2. Fox, L. and Southwell, R. V. (1945). Relaxation Methods Applied to Engineering Problems: VIIA. Biharmonic Analysis as Applied to the Flexure and Extension of Flat Elastic Plates. Phil. Trans., 239A, p. 419, 1945.Google Scholar
3. Thom, A. (1933). Arithmetical Solution of Equations of the Type = constant. R. & M. 1604, 1933.Google Scholar
4. Bickley, W. G. (1948). Finite Difference Formula for the Square Lattice. Quarterly Journal of Mechanics and Applied Mathematics, Vol. 1, p. 35.CrossRefGoogle Scholar
5. Woods, L. C. (1950). Improvements to the Accuracy of Arithmetical Solutions to Certain Two-dimensional Field Problems. Quarterly Journal of Mechanics and Applied Mathematics, Vol. 3, p. 349.CrossRefGoogle Scholar
6. Fox, L. (1947). Some Improvements in the Use of Relaxation Methods for the Solution of Ordinary and Partial Differential Equations. Proc. Roy. Soc, A, Vol. 190, p. 31, 1947.Google Scholar
7. Southwell, R. V. (1946). Relaxation Methods in Theoretical Physics, Oxford, 1946.Google Scholar
8. Thom, A. (1933). The Flow Past Circular Cylinders at Low Speeds. Proc. Roy. Soc, A, Vol. 141, p. 651, 1933.Google Scholar