A hybrid finite difference method for singularly perturbed delay partial
differential equations with discontinuous coefficient and source.
Abstract
The article presents a hybrid finite difference scheme to solve a
singularly perturbed parabolic functional differential equation with
discontinuous coefficient and source. The simultaneous presence of
deviating argument with a discontinuous source and coefficient makes the
problem stiff. The solution of the problem exhibits turning point
behaviour across discontinuity as ε tends to zero. The hybrid scheme
presented is a composition of a central difference scheme and a midpoint
upwind scheme on a specially generated mesh. At the same time, an
implicit finite difference method is used to discretize the time
variable. Consistency, stability, and convergence of the presented
numerical approach have been investigated. The presented method
converges uniformly independent of the perturbation parameter. Numerical
results have been presented for two test examples that verify the
effectiveness of the scheme.