Abstract
In this paper a refinement process is proposed, by means of which an approximate solution of a first order system of differential equations may be improved. The approximate solution should have been obtained with collocation on Gaussian points (cf. Russell [5]). Further, we discuss the equivalence of collocation for second order equations and collocation for the equivalent first order system. As a nice result, it is shown how we can obtain, withk collocation points per subinterval, approximations for the derivative of the solution of the second order equation with an error of orderO (h 2k ) in the nodes, using collocation for the second order equation. Finally, a numerical example is given.
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