In this study, a higher-order new approach numerical method for solving
singularly perturbed parabolic reaction-diffusion problems has
presented. To discretize time variable, we used the Crank-Nicolson
method on uniform mesh and space variable, we used hybrid numerical
method comprising a cubic spline tension method in the inner regions and
a central difference method in the outer region on Shishkin mesh. The
proposed method is proved to be uniformly convergent irrespective of the
perturbation parameter. Three numerical examples are computed to
validate the theoretical findings.