Picture of neon light reading 'Open'

Discover open research at Strathprints as part of International Open Access Week!

23-29 October 2017 is International Open Access Week. The Strathprints institutional repository is a digital archive of Open Access research outputs, all produced by University of Strathclyde researchers.

Explore recent world leading Open Access research content this Open Access Week from across Strathclyde's many research active faculties: Engineering, Science, Humanities, Arts & Social Sciences and Strathclyde Business School.

Explore all Strathclyde Open Access research outputs...

Defect estimation in Adams PECE codes

Higham, D.J. (1989) Defect estimation in Adams PECE codes. SIAM Journal on Scientific Computing, 10 (5). pp. 964-976. ISSN 1064-8275

Full text not available in this repository. Request a copy from the Strathclyde author

Abstract

Many modern codes for solving the nonstiff initial value problem $y'(x) - f(x,y(x)) = 0,y(a)$ given, $a leqq x leqq b$, produce, in addition to a discretised solution, a function $p(x)$ that approximates $y(x)$ over $[a,b]$. The associated defect $delta (x): = p'(x) - f(x,p(x))$ is a natural measure of the error. In this paper the problem of reliably estimating the defect in Adams PECE methods is considered. Attention is focused on the widely used Shampine-Gordon variable order, variable step code fitted with a continuously differentiable interpolant $p(x)$ due to Watts and Shampine [SIAM .J. Sci. Statist. Comput, 7 (1986), pp. 334-345]. It is shown that over each step an asymptotically correct estimate of the defect can be obtained by sampling at a single, suitably chosen point. It is also shown that a valid "free" estimate can be formed without recourse to sampling. Numerical results are given to support the theory.