Mathematical analysis derives vector error bounds for asymptotic solutions in first-order differential systems with distinct eigenvalues, facilitating precise limits on formal solution errors.
The method of Olver for bounding the error term in the asymptotic so lutions of a second-order equation having a n irregular singul arity at infinity is extended to the general system of n first-order equations in the case when the eige nvalu es of the lead coefficient matrix are distinct. Vector and norm bounds are given for th e difference between an actual solution vector and a partial su m of a for mal so luti on vector. Two cases are distinguished geometricall y: In one it is possible to exp ress the error vec tor by a s in gle Volterra vec tor integral equat.ion; in the other it is necessa ry to use a simultaneous pair of Volterra vector integral equatio ns. Some ne w inequaliti es for integral equations are given in an append ix .
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Frank Stenger (1966) studied this question.
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