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The recursive formulation of the Tau method is extended to the case of systems of ordinary differential equations, and an error analysis is given. Upper and lower error bounds are given in one of the examples considered. The asymptotic behavior of the error compares in this case with that of the best approximant by algebraic polynomials for each of the components of the vector solution.doi:10.2307/2007325 fatcat:m7xy7ya4cnaafar3g3yras6s3q