This paper proposes a uniformly convergent numerical method for a class of singularly perturbed turning point problems with a time-lag defined on a rectangular domain. We consider an interior repulsive turning point with odd multiplicity \(\geqslant 1\) . Twin boundary layers arise in the proximity of endpoints of the spatial domain due to the presence of the perturbation parameter. Preliminary results such as minimum principle, stability estimate, and solution derivative bounds for the continuous problem applicable in the convergence analysis are presented. First, we employ the Crank–Nicolson scheme to semi-discretize the continuous problem in the time direction, and then the cubic \(\mathscr {B}\) -spline functions on an appropriate Shishkin mesh are used to get a full discretization. The convergence analysis uses the maximum norm to obtain parameter-uniform error estimates. Three test problems are solved numerically to validate the theoretical results and confirm the scheme’s effectiveness.
