Numerical Method for Solving n Singularly Perturbed Mixed-Type Initial Value Problems with the Same Perturbation Parameter and Discontinuous Source Terms

This work examines a system of n singularly perturbed robin-type initial value problems with discontinuous source terms. Each equation’s derivative component is multiplied by the same singular perturbation parameter (ε). A piecewise uniform Shishkin mesh is built and used, together with a classical finite difference scheme, to create a numerical technique for addressing the problem. It is demonstrated that the numerical approximations produced by this method are effectively first order convergent in the maximum norm at all places in the domain, uniformly with regard to the singular perturbation parameter. Numerical findings are offered to support the theory.