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• W2113945807 abstract "A discrete approximation framework for initial-value problems involving certain classes of linear functional differential equations (FDE) of the retarded type is constructed. An equivalence between the FDE and abstract evolution equations (AEE) in an appropriately chosen Hilbert space is established. This equivalence is then employed in the development of discrete approximation schemes in which the infinite-dimensional AEE is replaced by a finite-dimensional system of difference equations. Convergence and rates of convergence are demonstrated via the properties of rational functions with operator arguments and both classical and recent results from linear semigroup theory. Two examples of families of approximation schemes which are included in the general framework and which may be implemented directly on high-speed computing machines are developed. A numerical study of examples which illustrates the application and feasibility of the approximation techniques in a variety of problems together with a summary and analysis of the numerical results are also included." @default.
• W2113945807 created "2016-06-24" @default.
• W2113945807 creator A5042461595 @default.
• W2113945807 date "1981-06-01" @default.
• W2113945807 modified "2023-10-16" @default.
• W2113945807 title "A discrete approximation framework for hereditary systems" @default.
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• W2113945807 doi "https://doi.org/10.1016/0022-0396(81)90004-8" @default.
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