Uniform Global Convergence of a Hybrid Scheme for Singularly Perturbed Reaction–Diffusion Systems

We consider a system of coupled singularly perturbed reaction–diffusion two‐point boundary‐value problems. A hybrid difference scheme on a piecewise‐uniform Shishkin mesh is constructed for solving this system, which generates better approximations to the exact solution than the classical central difference scheme. Moreover, we prove that the method is third order uniformly convergent in the maximum norm when the singular perturbation parameter is small. Numerical experiments are conducted to validate the theoretical results.