Differential-Difference Equations

Publisher Summary A systematic development of the theory of differential–difference equations was not begun until E. Schimdt published an important paper about fifty years ago. The subsequent gradual growth of the field has been replaced, in the last decade or so, by a rapid expansion due to the stimulus of various applications. This chapter introduces the study of differential–difference equations and discusses some of the main features of the theory. The role of differential–difference equations is vital in some areas, such as engineering problem and fluid mechanics. In engineering problem, the problem of controlling the temperature in a reaction tank is addressed using differential difference equations. The temperature variation is reported because of random disturbances, inherent effects due to u being non-zero, and the operation of the control device. The chapter discusses the asymptotic behavior of solutions and the problem of stability.

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