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The Quarterly Journal of Mechanics and Applied Mathematics 1956 9(3):371-383; doi:10.1093/qjmam/9.3.371
© 1956 by Oxford University Press
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THE DETERMINATION OF EIGENFUNCTIONS OF THE STORM-LIOIMLLE EQUATION EXPANSION IN TRIGONOMETRIC SERIES

S. C. R. DENNIS

( The Queen's University of Belfast )

In a recent paper (1) Dennis and Poots have given a particular numerical solution of a problem in heat transfer in which it is necessary to determine the discrete set of eigenvalues and associated eigenfunctions of an ordinary differential equation of Sturm-Liouville type. In the present paper an attempt is made to standardize the analysis to deal with a more general Sturm-Liouville system, and to point out the possibility of a feasible general numerical method of approach. The eigenfunctions are expressed as infinite series of trigonometrical functions, orthogonal over a finite interval of integration, and the Sturm-Liouville equation is reduced to an infinite set of linear simultaneous algebraic equations for the coefficients of the series. These equations contain the characteristic parameter, and may be solved by standard iterative or relaxation methods. Two numerical examples are treated in detail.


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