Non-standard numerical scheme for singularly perturbed parabolic partial
differential equation with long time lag arising in control theory
Abstract
For the numerical solution of singularly perturbed second-order
parabolic partial differential equation of one dimensional
convection-diffusion type with long time delays arising in control
theory, a novel class of fitted operator finite difference methods is
constructed using non-standard finite difference methods. Since the two
parameters; time lag and perturbation parameters are sources for the
simultaneous occurrence of time-consuming and high speed phenomena of
the physical systems that depends on the present and past history, our
study here is to capture the effect of the two parameters on the
boundary layer. The spatial derivative is suitably replaced by a
difference operator followed by the time derivative is replaced by the
Crank-Nicolson based scheme. A second-order parameter-uniform error
bounds are established to provide numerical results.