On the exact and numerical solution of the time-delayed Burgers equation

A number of nonlinear phenomena in many branches of sciences such as physical [6], chemical, economical [20] and biological processes [15,14] are described by the interplay of reaction and diffusion or by the interaction between convection and diffusion. One of the well-known partial differential equations (PDEs) which governs a wide variety of them is Burgers equation, which provides the simplest nonlinear model of turbulence [5]. The existence of relaxation time or delay time is an important feature in reaction diffusion and convection diffusion systems [9,1,3]. The generalized time-delayed Burgers–Fisher equation can be derived by a similar manner to that presented in [9]. It takes the following form: