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The Computer Journal 1971 14(3):270-271; doi:10.1093/comjnl/14.3.270
© 1971 by British Computer Society
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A note on the integration of ordinary differential equations using Chebyshev series

R. A. C. Boggs * and F. J. Smith *

Computer Science Department, The Queen's University of Belfast, Belfast, UK

By using two different forms of residual, we obtain two differing versions of Lanczos' {tau}-method. We examine the collocation method using the zeros of a Chebyshev polynomial as pivots, and show that it is equivalent to the less accurate of the two {tau}-methods; the other {tau}-method is equivalent to Clenshaw's Chebyshev method.

We note an unusual feature of these solutions when solving some unstable equations.

Received December 1969.

* Computer Science Department, The Queen's University of Belfast, Belfast, N. Ireland


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