A singularly perturbed parabolic problem with a layer in the initial condition

Abstract

Singularly perturbed reaction–diffusion parabolic problems with non-smooth initial conditions are studied. A finite difference method is constructed on a piecewise-uniform mesh for a parabolic problem with an initial condition containing a layer. The parameter-uniform convergence of this numerical method is analyzed. This numerical method is used to generate an approximation to the solution of a singularly perturbed parabolic problem with a discontinuous initial condition.