A parameter uniform difference scheme for singularly perturbed parabolic problem in one space dimension (Q864738)

The authors propose a numerical method for singularly perturbed one-dimensional parabolic convection-diffusion initial-boundary-value problems. The spatial domain is discretized with a piecewise-uniform Shishkin mesh, and the time domain with a uniform mesh. The Crank-Nicolson finite difference scheme is applied on this mesh for the parabolic partial differential equation. A parameter-uniform error estimate of order \(O(N_x^{-1}(\ln N_x)^2 + N_t^{-2})\) is derived. Some numerical examples are tested to verify the theoretical results.