Linear differential difference equations

Abstract

In this chapter, we discuss the simplest possible differential difference equations; namely, linear equations with constant coefficients. For these equations, a rather complete theory can be developed using very elementary tools. The chapter serves as an introduction to the more general types of equations that will be encountered in later chapters. It also is intended to bring out the roles of the characteristic equation and the Laplace transform, and to emphasize some of the differences between retarded and neutral equations. Since ordinary differential equations and difference equations are special cases of the theory, we begin the discussion with the latter.KeywordsInitial DataOrdinary Differential EquationDifference EquationCharacteristic EquationFundamental SolutionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.