We study an initial-boundary value problem for a singularly perturbed reaction–convection–diffusion system. Asymptotic analysis is used to construct a domain decomposition method for the system to describe the asymptotic nature of the interactions between the boundary layers, interior layers and shock layers. Our results show that the formation of boundary layers and shock layers depends upon i...

HIV evolution model that describes the dynamics of concentrations of uninfected and infected cells is considered in the paper. The introduction of dimensionless variables and parameters leads to the initial boundary value problem for singularly perturbed system of partial integro-differential equations. By Tikhonov-Vasil’eva boundary functions method asymptotic solution with boundary layer is c...

We give a new proof that the El-Mistikawy and Werle finite-difference scheme is uniformly second-order accurate for a nonselfadjoint singularly perturbed boundary value problem. To do this, we use exponential finite elements and a discretized Green's function. The proof is direct, gives the nodal errors explicitly in integral form, and involves much less computation than in previous proofs of t...