Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-03T05:35:38.971Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Theory of Relaxation

Published online by Cambridge University Press:  18 May 2009

A. R. Mitchell  and
D. E. Rutherford
A. R. Mitchell
Affiliation:
United College St. Andeews
D. E. Rutherford
Affiliation:
United College St. Andeews
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

§ 1. When a numerical method of obtaining an approximate solution of a linear differential equation is employed, the process involves two distinct types of approximation. The region of integration having been covered with a regular net, the differential equation and the appropriate boundary conditions are replaced by finite difference equations which are linear equations in the values of the dependent variable at the nodes of the net.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 1 , Issue 3 , September 1953 , pp. 101 - 110
Copyright
Copyright © Glasgow Mathematical Journal Trust 1953

References

REFERENCES

(1)Courant, R., Friedrichs, K., and Lewy, H., Math. Annalen, 100, (1928), pp. 32–74.CrossRefGoogle Scholar
(2)O'Brien, G. G., Hyman, M. A., and Kaplan, S., Jour. Math, and Phys., 29 (1951), pp. 223–251.CrossRefGoogle Scholar
(3)Thomas, L. H., “Symposium on Theoretical Compressible Flow, 1949,” White Oak, Maryland.Google Scholar
(4)Rutishauser, H., Zeit. f. angewandte Math. u. Phys., 3 (1952), pp. 65–74.CrossRefGoogle Scholar
(5)Bickley, W. G., Math. Gaz., 25 (1941), pp. 19–27.CrossRefGoogle Scholar
(6)Bickley, W. G., Q.J. Mech. App. Math., 1 (1948), pp. 35–42.CrossRefGoogle Scholar
(7)Rutherford, D. E., Proc. Roy. Soc. Edin., (A) 63 (1952), pp. 232–241.Google Scholar
(8)Temple, G., Proc. Roy. Soc., (A) 169 (1939), pp. 476–500.Google Scholar
(9)Stiefel, E., Zeit. f. angewandte Math. u. Phys., 3 (1952), pp. 1–33.CrossRefGoogle Scholar
(10)Fox, L., Q.J. Mech. App. Math., 1 (1948), pp. 253–280.CrossRefGoogle Scholar
(11)Southwell, R. V., Relaxation Methods in Theoretical Physics, Oxford (1946).Google Scholar
(12)Turing, A. M., Q.J. Mech. App. Math., 1 (1948), pp. 287–308.CrossRefGoogle Scholar
(13)Todd, J., Proc. Comb. Phil. Soc., 46 (1949), pp. 116–118.CrossRefGoogle Scholar
(14)von Neumann, J. and Goldstine, H. H., Bull. Amer. Math. Soc., 53 (1947), pp. 1021–1099.CrossRefGoogle Scholar
(15)Allen, D. N. de G., and Severn, R. T., Q.J. Mech. App. Math., 4 (1951), pp. 209–222.CrossRefGoogle Scholar