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The numerical solution of linear differential equations in Chebyshev series

Published online by Cambridge University Press:  24 October 2008

C. W. Clenshaw
C. W. Clenshaw
Affiliation:
National Physical Laboratory Teddington, Middlesex
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Abstract

This paper describes a method for computing the coefficients in the Chebyshev expansion of a solution of an ordinary linear differential equation. The method is valid when the solution required is bounded and possesses a finite number of maxima and minima in the finite range of integration. The essence of the method is that an expansion in Chebyshev polynomials is assumed for the highest derivative occurring in the equation; the coefficients are then determined by integrating this series, substituting in the original equation and equating coefficients.

Comparison is made with the Fourier series method of Dennis and Foots, and with the polynomial approximation method of Lanczos. Examples are given of the application of the method to some first and second order equations, including one eigenvalue problem.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 53 , Issue 1 , January 1957 , pp. 134 - 149
Copyright
Copyright © Cambridge Philosophical Society 1957

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References

REFERENCES

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