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

2003
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Quarterly of Applied Mathematics
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Given an initial approximation <&0 to the fundamental matrix of solutions for = A(t), it is shown that a left correction, T^o, is locally more accurate than a right correction, ^oT. For each relative error function considered, there is a left correction r 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. Upon transformation into a Volterra integral

doi:10.1090/qam/1999836
fatcat:u4lojhopujfz3jgjlyfnhyh3aq