Parameter-uniform numerical scheme for singularly perturbed parabolic convection–diffusion Robin type problems with a boundary turning point

In this work, a numerical method for the singularly perturbed parabolic convection–diffusion turning point problem with Robin boundary condition was developed. The solution to the considered problem has a boundary layer on the left side of the domain. The present method comprises an implicit trapezoidal method for time discretization on a uniform mesh and second-order central difference schemes for space discretization on a Shishkin mesh. The resultant scheme has been shown that the numerical approximation converges uniformly to the solution of the continuous problem regardless of the diffusion parameter. Finally, to validate the resultant scheme, numerical experiments were performed.