A fast uniformly accurate global numerical approximation to solution and scaled derivative of system of singularly perturbed problems with multiple diffusion parameters on generalized adaptive mesh

The aim of this article is to analyze a robust numerical approximation to the solution along with the scaled first derivative (physically known as diffusive flux ) of its components of a weakly coupled system of singularly perturbed convection-diffusion boundary-value-problems having diffusion parameters of different orders of magnitude. To accomplish this, we construct a generalized S-mesh, a general form of the piecewise-uniform Shishkin mesh, which appropriately resolves the overlapping boundary layers caused by the multiple diffusion parameters. For discretizing the governing system of equations, we confine our study to the upwind finite difference scheme. At first, we prove that the numerical solution converges uniformly in C 0 -norm with faster convergence rate on the generalized S-mesh than the standard Shishkin mesh. Afterwards, we prove uniform convergence of the global numerical approximation in an appropriate weighted C 1 -norm with same order of accuracy, which essentially establishes global accuracy to the numerical solution as well as the scaled discrete derivative. We confirm the theoretical findings by conducting extensive numerical experiments on two test examples for both equal and unequal values of diffusion parameters.