AbstractNew high-order accurate finite difference schemes based on defect correction are considered for an initial boundary-value problem on an interval for singularly
perturbed parabolic PDEs with convection; the highest space derivative in the equation is multiplied by the perturbation parameter ε. Solutions of the
well-known classical numerical schemes for such problems do not converge ε-uniformly (the errors of such schemes depend on the value of the parameter ε and are comparable
with the solution itself for small values of ε). The convergence order of the existing ε-uniformly convergent schemes does not exceed 1 in space and time. In this paper,
using a defect correction technique, we construct a special difference scheme that converges ε-uniformly with the second (up to a logarithmic factor) order of accuracy with
respect to x and with the second order of accuracy and higher with respect to t.
A generalized regularization scheme for solving singularly perturbed parabolic PDEs
