Defect estimation in Adams PECE codes
Higham, D.J. (1989) Defect estimation in Adams PECE codes. SIAM Journal on Scientific Computing, 10 (5). pp. 964976. ISSN 10648275 (https://doi.org/10.1137/0910056)
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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 ShampineGordon 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. 334345]. 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.
ORCID iDs
Higham, D.J. ORCID: https://orcid.org/0000000266353461;

Item type: Article ID code: 212 Dates: DateEvent1989PublishedKeywords: Adams PECE method, interpolant, defect, numerical mathematics, Probabilities. Mathematical statistics, Computational Mathematics, Applied Mathematics Subjects: Science > Mathematics > Probabilities. Mathematical statistics Department: Faculty of Science > Mathematics and Statistics Depositing user: Ms Sarah Scott Date deposited: 08 Mar 2006 Last modified: 18 Jan 2023 08:21 URI: https://strathprints.strath.ac.uk/id/eprint/212