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The purpose of this paper is to introduce a new spline approximation scheme for retarded functional differential equations. The special feature of this approximation scheme is that it preserves the product space structure of retarded systems and approximates the adjoint semigroup in a strong sense. These facts guarantee the convergence of the solution operators for the differential Riccati equation in a strong sense. Numerical findings indicate a significant improvement in the convergence behaviour over both the averaging and the previous spline approximation scheme.

Spline Approximation for Retarded Systems and the Riccati Equation