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A new spline-based scheme is developed for linear retarded functional differential equations within the framework of the semigroups on the Hilbert space Rn ? L2. The approximating semigroups preserve (uniformly) the logarithmic sectorial property (i.e., the differentiability) of the solution semigroup. We prove the convergence of the scheme both in W1,2, Rn ? L2, and using the uniform differentiability...
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