Abstract
A collocation method for initial value problems, parametrized byn + 1, the number of collocation points, and δ, the step size, is shown (using Kantorovich's methods) to produce errors which are uniformlyO[δ/n]p+1 for linear time varying systems of ordinary differential equations whose solutions arepth order continuous. Using Wright's method, the single step error is shown to yield errors which areO[δn+k+2 for anyk, 0 <k <n, by suitable choice of the collocation points.
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Wouk, A. Collocation for initial value problems. BIT 16, 215–222 (1976). https://doi.org/10.1007/BF01931372
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DOI: https://doi.org/10.1007/BF01931372