A collocation procedure with polynomial and piecewise polynomial approximation is considered for second order functional differential equations with two side-conditions. The piecewise polynomials are taken in the classC1 and reduce to polynomials of increasing degree on each interval of a suitable assigned partition. Appropriate choices of the partition are made, according to the jump discontinuities in the derivatives caused by the functional argument, in order to optimize the rate of convergence.ZusammenfassungEs wird eine Kollokationsmethode mit polynomialer und stückweise polynomialer Approximation für Funktional-Differentialgleichungen zweiter Ordnung mit zweiseitigen Bedingungen betrachtet. Die stückweisen Polynome werden in der KlasseC1 genommen und bestehen aus Polynomen mit ansteigendem Grad in jedem Intervall einer günstig gegebenen Partition. Günstige Wahlen der Partition werden gemacht, gemäß der Diskontinuitäten der Ableitungen, die durch die Funktional-Argumente verursacht werden, dermaßen, daß die Konvergenzgeschwindigkeit optimal werde.
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