AbstractThe boundary-value problem for a singularly perturbed parabolic PDE
with convection is considered on an interval in the case of the singularly perturbed
Robin boundary condition; the highest space derivatives in the equation and in the
boundary condition are multiplied by the perturbation parameter ε. The order of convergence
for the known ε-uniformly convergent schemes does not exceed 1. In this paper, using
a defect correction technique, we construct ε-uniformly convergent schemes of highorder
time-accuracy. The efficiency of the new defect-correction schemes is confirmed
by numerical experiments. A new original technigue for experimental studying of
convergence orders is developed for the cases where the orders of convergence in the
x-direction and in the t-direction can be substantially different.
THE NUMERICAL SOLUTION OF A NEUMANN PROBLEM FOR PARABOLIC SINGULARLY PERTURBED EQUATIONS WITH HIGH-ORDER TIME ACCURACY
