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On matrix methods for the solution of partial differential equations

Published online by Cambridge University Press:  24 October 2008

M. Wadsworth  and
A. Wragg
M. Wadsworth
Affiliation:
Royal College of Advanced Technology, Salford
A. Wragg
Affiliation:
Royal College of Advanced Technology, Salford
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Extract

Bickley and McNamee (1) describe techniques for obtaining the solution of finite difference equations, arising from partial differential equations, making extensive use of matrix methods. In all cases solutions are obtained by solving algebraic equations as distinct from differential equations. For example, in order to solve

the second space derivative is replaced by finite differences and the time derivative is replaced either by substituting the backward finite difference form or by using the Laplace transformation.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 61 , Issue 1 , January 1965 , pp. 129 - 132
Copyright
Copyright © Cambridge Philosophical Society 1965

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References

REFERENCES

(1)Bickley, W. G. and McNamee, J.Philos. Trans. Roy. Soc. London, Ser. A 252 (1960), 69–131.Google Scholar
(2)Carslaw, H. S. and Jaeger, J. C.Conduction of heat in solids (Oxford, 1947).Google Scholar
(3)Peaceman, D. W. and Rachford, H. H.J. Soc. Indust. Appl. Math. 3 (1955), 28–41.Google Scholar
(4)Wadswobth, M. and Wragg, A.Proc. Cambridge Philos. Soc. (to appear).Google Scholar