Abstract <p>Nonlinear science plays a vital role in modern technology. Due to the limitations over the linear theories, the analysis of nonlinear problems has become very essential to investigate the dynamics of complicated and multi parameter problems. This article aims at the analysis and implementation of a numerical method for a class of two parameter singularly perturbed nonlinear differential equations with Cauchy data. A non-classical, robust and layer-resolving numerical method involving the continuation algorithm is developed to obtain the numerical approximations to the class of problems. The newly developed numerical method is proved to be essentially first order convergent uniformly with respect to the parameters. Numerical experiments included support the theoretical results.</p>