Overlapping Iterative Numerical Method for Solving System of Singularly Perturbed Convection-Diffusion Problems with Mixed-Type Boundary Conditions

In this article, using an overlapping iterative numerical technique on a Shiskin-type mesh, we study the convergence of a system of singularly perturbed convection-diffusion equations (SSPCDEs) with mixed-type boundary conditions (MBCs). The study is based on the definition of a few auxiliary problems that demonstrate the method’s uniform convergence in two steps and distinguish between the discretization and iteration errors. Using the supremum norm, an error estimate of order \( O ({\textsf{N}^{-1}} {\ln }^{2} {\textsf{N}})\) is deduced. The hypothetical results are demonstrated by numerical experiments.