Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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$ L$-derivative of an approximate solution to $ \Phi '=\bold A(t)\Phi $: series and product formulae for left corrections


Authors: Igor Najfeld and William Lakin
Journal: Quart. Appl. Math. 61 (2003), 537-564
MSC: Primary 34A45; Secondary 34A30, 45D05
DOI: https://doi.org/10.1090/qam/1999836
MathSciNet review: MR1999836
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Abstract: Given an initial approximation $ {\Phi _0}$ to the fundamental matrix of solutions for $ \Phi ' = {\rm A}\left( t \right)\Phi $, it is shown that a left correction, $ \Gamma {\Phi _0}$, is locally more accurate than a right correction, $ {\Phi _0}\Gamma $. For each relative error function considered, there is a left correction $ \Gamma $ and the associated differential equation. The common feature is the same integrable part whose forcing function is the difference between L-derivatives of the exact and the initial solution.


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DOI: https://doi.org/10.1090/qam/1999836
Article copyright: © Copyright 2003 American Mathematical Society


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