Cen, ZhongdiErdogan, FevziXu, Aimin2025-05-102025-05-1020141017-13981572-926510.1007/s11075-013-9801-02-s2.0-84910154060https://doi.org/10.1007/s11075-013-9801-0https://hdl.handle.net/20.500.14720/15782In this paper a nonlinear singularly perturbed initial problem is considered. The behavior of the exact solution and its derivatives is analyzed, and this leads to the construction of a Shishkin-type mesh. On this mesh a hybrid difference scheme is proposed, which is a combination of the second order difference schemes on the fine mesh and the midpoint upwind scheme on the coarse mesh. It is proved that the scheme is almost second-order convergent, in the discrete maximum norm, independently of singular perturbation parameter. Numerical experiment supports these theoretical results.eninfo:eu-repo/semantics/closedAccessSingular PerturbationInitial Value ProblemFinite Difference SchemeShishkin MeshUniform ConvergenceArticle672Q1Q1457476WOS:000342492300012