AN EFFICIENT NUMERICAL ALGORITHM FOR A NONLINEAR SYSTEM OF SINGULARLY PERTURBED DIFFERENTIAL EQUATIONS

Nonlinear science plays a vital role in modern technology. Due to the limitations over the linear theories and the chaotic nature of the problems in this technological era, the analysis of nonlinear problems has become extremely essential to investigate the dynamics of complicated and multiscale characteristics systems. In this article, a nonlinear system of singularly perturbed differential equations with Dirichlet boundary conditions is considered. Both components of the system exhibit a strong boundary layer near the boundary \(t = 0\) $t=0$ of the domain, even though a perturbation parameter occurs only in one of the equations of the system. A robust and layer-resolving numerical method involving the continuation technique is constructed to obtain the numerical approximations to the system. The newly developed numerical method is shown to be first-order convergent uniformly with respect to the perturbation parameter.