Approximation of Functional Differential Equations by Differential Systems

摘要

Functional differential equations were introduced to analyze systems whose future behavior was dependent on past states. A dispute has periodically erupted concerning the propriety of explicitly including hereditary influences in models of physical systems. This report establishes that given any retarded functional differential equation, one can construct a reducible system or, equivalently, a system of ordinary differential equations, whose solutions approximate those of the delay equation to any prescribed degree of accuracy. (ERA citation 07:055039)