Project Description

Singularly perturbed delay partial differential equations (SPDPDEs) arise from many biological, chemical and physical systems which are characterized by both spatial and temporal variables and exhibit various spatio-temporal patterns. One such model is of the automatically controlled furnace in which time delay and spatial diffusion enter the control system. SPDPDEs model problems, whose solution not only depends on the present state of the system but also on the past history. The solution of the equation may behave quite differently from the solution of the approximate singularly perturbed PDE obtained by replacing the shift terms with first few terms of Taylor series. Small lags can have large effects.

Under this research project, two classes of SPDPDEs are considered for numerical study, the one with a negative shift in the temporal variable and the other with negative and positive shifts in the space variable. The proposed methods will be analysed for stability and convergence. All the proposed numerical methods will be implemented on the physical problems and efficiency of the methods will be demonstrated.